X-ray Binary Luminosity Function Scaling Relations for Local Galaxies Based on Subgalactic Modeling

TL;DR

This study uses Chandra data to analyze X-ray binary luminosity functions across 38 nearby galaxies, revealing complex dependencies on galaxy properties like star formation rate, stellar mass, metallicity, and globular cluster content.

Contribution

It introduces a global XLF model that accounts for contributions from HMXBs, LMXBs, and background sources, and explores their dependence on galaxy-scale parameters.

Findings

HMXB XLF shape is more complex than previously thought.

LMXB XLF likely varies with specific SFR, indicating age dependence.

Galaxies with low metallicity or rich globular clusters show deviations from the global model.

Abstract

We present new Chandra constraints on the X-ray luminosity functions (XLFs) of X-ray binary (XRB) populations, and their scaling relations, for a sample of 38 nearby galaxies (D = 3.4-29 Mpc). Our galaxy sample is drawn primarily from the Spitzer infrared nearby galaxy survey (SINGS), and contains a wealth of Chandra (5.8 Ms total) and multiwavelength data, allowing for star-formation rates (SFRs) and stellar masses (M*) to be measured on subgalactic scales. We divided the 2478 X-ray detected sources into 21 subsamples in bins of specific-SFR (sSFR = SFR/M*) and constructed XLFs. To model the XLF dependence on sSFR, we fit a global XLF model, containing contributions from high-mass XRBs (HMXBs), low-mass XRBs (LMXBs), and background sources from the cosmic X-ray background (CXB) that respectively scale with SFR, M*, and sky area. We find an HMXB XLF that is more complex in shape than previously reported and an LMXB XLF that likely varies with sSFR, potentially due to an age dependence. When applying our global model to XLF data for each individual galaxy, we discover a few galaxy XLFs that significantly deviate from our model beyond statistical scatter. Most notably, relatively low-metallicity galaxies have an excess of HMXBs above ~10^38 erg/s and elliptical galaxies that have relatively rich populations of globular clusters (GCs) show excesses of LMXBs compared to the global model. Additional modeling of how the XRB XLF depends on stellar age, metallicity, and GC specific frequency is required to sufficiently characterize the XLFs of galaxies.

Tables

Table 1. Table 1: Nearby Galaxy Sample and Properties

Galaxy						Size Parameters
Name	Alt.	Morph.	Central Position		$D$	$a$	$b$	PA	$r_{\_}\mathrm{remove}$	SFR	$\log M_{\_}\star$	$\log$ sSFR	12 + $\log$ [O/H]
(NGC)	Name	Type	${\alpha }_{\_}\mathrm{J2000}$	${\delta }_{\_}\mathrm{J2000}$	(Mpc)	(arcmin)	(arcmin)	(deg)	(arcsec)	($M_{\_}\odot$ yr-1)	($M_{\_}\odot$)	(${\mathrm{yr}}^{-1}$)	(dex)	$S_{\_}N$
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)
337		SBd	00 59 50.1	$-$07 34 40.7	22.40$\pm$2.30	0.87	0.49	$-$22.5	0	1.09	9.32	$-$9.28	8.44$\pm$0.07	…
584		E4	01 31 20.8	$-$06 52 05.0	20.10$\pm$1.90	1.47	0.91	62.5	0	0.05	10.48	$-$11.77	8.75∗	1.69$\pm$0.67
628	M74	SAc	01 36 41.8	+15 47 00.5	7.30$\pm$1.40	2.10	1.80	87.5	3	0.33	9.48	$-$9.96	8.54$\pm$0.15	…
925		SABd	02 27 16.9	+33 34 44.0	9.12$\pm$0.17	1.87	0.82	$-$75.0	0	0.18	9.03	$-$9.78	8.38$\pm$0.15	…
1097		SBb	02 46 19.1	$-$30 16 29.7	17.10$\pm$2.30	2.63	1.44	$-$35.0	5	4.51	10.76	$-$10.11	8.83$\pm$0.05	…
1291		SB0/a	03 17 18.6	$-$41 06 29.1	10.80$\pm$2.30	2.39	1.70	$-$10.0	3	0.08	10.81	$-$11.89	9.20∗	…
1316		SAB0	03 22 41.8	$-$37 12 29.5	21.50$\pm$1.70	2.77	1.99	47.5	3	0.49	11.48	$-$11.79	9.52∗	0.54$\pm$0.27
1404		E1	03 38 51.9	$-$35 35 39.8	20.80$\pm$1.70	1.38	1.24	$-$17.5	3	0.10	10.98	$-$11.99	9.21∗	1.78$\pm$0.32
2841		SAb	09 22 02.7	+50 58 35.3	14.10$\pm$1.50	3.02	1.36	$-$30.0	0	0.61	10.67	$-$10.89	8.89$\pm$0.05	…
3031	M81	SAab	09 55 33.2	+69 03 54.9	3.55$\pm$0.13	8.13	4.14	$-$31.0	12	0.25	10.39	$-$10.98	8.60$\pm$0.09	1.11$\pm$0.37
3184		SABcd	10 18 17.0	+41 25 27.8	11.10$\pm$1.90	1.91	1.62	117.5	0	0.48	9.68	$-$10.00	8.75$\pm$0.12	…
3198		SBc	10 19 55.0	+45 32 58.9	13.68$\pm$0.50	1.91	0.67	40.0	0	0.55	9.70	$-$9.96	8.43$\pm$0.15	…
3351	M95	SBb	10 43 57.7	+11 42 13.0	9.33$\pm$0.39	1.94	1.71	$-$17.0	0	0.57	9.95	$-$10.19	9.21$\pm$0.05	…
3521		SABbc	11 05 48.6	$-$00 02 09.2	10.10$\pm$2.30	2.74	1.40	$-$14.5	0	1.43	10.41	$-$10.25	8.74$\pm$0.09	…
3627	M66	SABb	11 20 15.0	+12 59 28.6	9.38$\pm$0.35	3.08	1.70	6.5	3	1.83	10.30	$-$10.04	8.66$\pm$0.11	…
3938		SAc	11 52 49.5	+44 07 14.6	13.40$\pm$2.30	1.30	1.23	28.5	0	0.58	9.64	$-$9.88	8.74∗	…
4125		E6 pec	12 08 06.0	+65 10 26.9	23.90$\pm$2.80	1.76	1.11	82.5	0	0.13	10.84	$-$11.73	9.30∗	…
4254	M99	SAc	12 18 49.6	+14 24 59.4	16.50$\pm$0.60	1.70	1.62	23.5	0	3.17	10.21	$-$9.71	8.77$\pm$0.11	…
4321	M100	SABbc	12 22 54.9	+15 49 20.6	14.32$\pm$0.46	2.51	1.96	$-$72.5	0	2.04	10.24	$-$9.93	8.81$\pm$0.07	…
4450		SAab	12 28 29.6	+17 05 05.3	16.50$\pm$0.60	1.87	1.18	2.5	3	0.19	10.40	$-$11.12	8.82∗	…
4536		SABbc	12 34 27.1	+02 11 16.4	14.45$\pm$0.27	1.89	0.98	$-$85.0	0	1.88	10.13	$-$9.86	8.45$\pm$0.23	…
4552	M89	E	12 35 39.9	+12 33 21.7	15.92$\pm$0.81	1.48	1.39	$-$30.0	3	0.08	10.54	$-$11.66	8.83∗	7.68$\pm$1.40
4559		SABcd	12 35 57.7	+27 57 35.1	10.30$\pm$2.30	2.04	0.96	$-$32.5	0	0.45	9.34	$-$9.68	8.40$\pm$0.13	…
4569		SABab	12 36 49.8	+13 09 46.3	16.50$\pm$0.60	2.75	1.10	15.0	2	1.06	10.48	$-$10.45	9.26∗	…
4594	M104	SAa	12 39 59.5	$-$11 37 23.1	9.33$\pm$0.34	3.36	1.82	87.5	3	0.18	10.86	$-$11.59	9.22∗	2.70$\pm$0.28
4725		SABab pec	12 50 26.6	+25 30 02.7	11.91$\pm$0.33	2.91	1.51	50.0	0	0.37	10.38	$-$10.81	8.79$\pm$0.08	…
4736	M94	SAab	12 50 53.1	+41 07 12.5	5.20$\pm$0.43	2.87	2.27	85.0	0	0.50	10.13	$-$10.43	8.72$\pm$0.04	…
4826	M64	SAab	12 56 43.7	+21 40 57.6	7.48$\pm$0.69	3.58	2.04	$-$70.0	0	0.42	10.41	$-$10.79	9.24$\pm$0.04	…
5033		SAc	13 13 27.5	+36 35 37.1	14.80$\pm$2.30	1.79	0.80	$-$5.0	5	0.84	10.37	$-$10.44	8.55$\pm$0.13	…
5055	M63	SAbc	13 15 49.3	+42 01 45.4	7.80$\pm$2.30	3.40	1.97	$-$82.5	0	0.94	10.26	$-$10.29	8.80$\pm$0.10	…
5194	M51	SABbc pec	13 29 52.7	+47 11 42.9	8.58$\pm$0.10	3.29	2.24	57.5	3	2.61	10.24	$-$9.83	8.87$\pm$0.11	0.76$\pm$0.15
5236	M83	SABc	13 37 00.9	$-$29 51 56.7	4.66$\pm$0.33	5.21	4.01	45.0	0	2.48	10.33	$-$9.94	8.95$\pm$0.03‡	0.17$\pm$0.05
5457	M101	SABcd	14 03 12.5	+54 20 55.5	6.81$\pm$0.03	3.94	3.90	28.5	0	1.07	9.91	$-$9.88	9.10$\pm$0.08‡	0.43$\pm$0.11
5713		SABbc pec	14 40 11.5	$-$00 17 21.2	29.40$\pm$2.30	0.90	0.89	$-$20.0	0	5.48	10.15	$-$9.41	8.63$\pm$0.06	…
5866	M102	S0	15 06 29.6	+55 45 47.9	15.42$\pm$0.85	1.86	0.78	$-$57.0	0	0.14	10.46	$-$11.32	8.81∗	1.37$\pm$0.26
6946		SABcd	20 34 52.3	+60 09 13.2	6.80$\pm$1.70	4.21	2.95	52.5	0	2.46	10.01	$-$9.61	8.66$\pm$0.11	0.29$\pm$0.13
7331		SAb	22 37 04.1	+34 24 57.3	14.52$\pm$0.60	2.60	1.27	$-$12.5	0	2.12	10.75	$-$10.42	8.73$\pm$0.05	0.43$\pm$0.27
7552		SBab	23 16 10.8	$-$42 35 05.4	21.00$\pm$2.30	1.27	0.75	$-$85.0	15	3.58	10.04	$-$9.48	8.85$\pm$0.01	…
Total	…	…	…	…	…	…	…	…	…	45.4	12.10	$-$10.44	…	…

Table 2. Table 2: Chandra  Advanced CCD Imaging Spectrometer (ACIS) Observation Log

	Aim Point		Obs. Start	Exposurea	Flaringb	$\Delta \alpha$	$\Delta \delta$	Obs.
Obs. ID	${\alpha }_{\_}\mathrm{J2000}$	${\delta }_{\_}\mathrm{J2000}$	(UT)	(ks)	Intervals	(arcsec)	(arcsec)	Modec
NGC0337
12979d	00 59 49.29	$-$07 34 28.15	2011-07-19T23:07:02	10	…	…	…	F
NGC0584
12175d	01 31 20.38	$-$06 51 38.45	2010-09-07T01:40:53	10	…	…	…	V
NGC0628
14801	01 36 47.41	+15 45 32.58	2013-08-21T15:40:51	10	…	$+$0.05	$+$0.01	V
16000	01 36 47.37	+15 45 31.61	2013-09-21T06:40:27	40	…	$+$0.56	$-$0.24	V
16001	01 36 47.39	+15 45 29.57	2013-10-07T23:56:17	15	…	$+$0.24	$-$0.07	V
16002	01 36 48.85	+15 45 26.66	2013-11-14T20:10:48	38	…	$+$0.08	$+$0.16	V
16003	01 36 48.89	+15 45 28.36	2013-12-15T15:55:42	40	…	$+$0.04	$-$0.11	V
16484	01 36 47.38	+15 45 29.36	2013-10-10T14:31:23	15	…	$+$0.45	$+$0.14	V
16485	01 36 47.39	+15 45 29.44	2013-10-11T11:13:35	9	…	$+$0.32	$+$0.06	V
2057	01 36 40.35	+15 48 17.73	2001-06-19T19:03:09	46	1, 0.5	$-$0.05	$-$0.05	F
2058d	01 36 36.11	+15 46 51.99	2001-10-19T04:08:30	46	…	…	…	F
4753	01 36 51.21	+15 45 12.44	2003-11-20T04:14:02	5	…	$-$0.10	$-$0.03	F
4754	01 36 51.51	+15 45 12.89	2003-12-29T13:07:58	5	…	$+$0.09	$+$0.07	F
Mergede	01 36 44.82	+15 46 11.67		269	1, 0.5	…	…	…

Table 3. Table 3: X-ray Luminosity Function Fits By Galaxy

Galaxy					Single Power Law†				Broken Power Law‡
Name	Alt		$\log L_{\_}50$	$\log L_{\_}90$										Model	$\log L_{\_}X$
(NGC)	Name	$N_{\_}\mathrm{src}$	(erg s-1)	(erg s-1)	$K_{\_}\mathrm{PL}$	$\alpha$	$C$	$P_{\_}\mathrm{Null}$	$K_{\_}\mathrm{BKNPL}$	${\alpha }_{\_}1$	${\alpha }_{\_}2$	$C$	$P_{\_}\mathrm{Null}$	(S B)	(ergs s-1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)	(16)
337		6	38.5	38.7	6.0${}_{\_}{}^{+12.6}-4.6$	1.49${}_{\_}{}^{+0.42}-0.31$	22	0.944	8.08${}_{\_}{}^{+3.74}-3.00$	1.60∗	1.60∗	23	0.889	B	40.4$\pm$0.2
584		7	38.5	38.7	193${}_{\_}{}^{+504}-151$	3.60${}_{\_}{}^{+0.88}-0.99$	11	0.686	21.0${}_{\_}{}^{+12.4}-9.2$	1.20∗	2.20∗	9	0.169	B	40.0$\pm$0.2
628	M74	43	36.4	36.6	1.51${}_{\_}{}^{+0.67}-0.55$	1.68${}_{\_}{}^{+0.16}-0.14$	31	0.106	4.16${}_{\_}{}^{+2.16}-1.58$	1.25$\pm$0.21	4.05${}_{\_}{}^{+0.66}-0.95$	26	0.109	B	38.9$\pm$0.2
925		7	37.5	37.7	1.47${}_{\_}{}^{+1.02}-0.72$	1.37${}_{\_}{}^{+0.26}-0.24$	26	0.785	1.03${}_{\_}{}^{+0.82}-0.52$	2.28${}_{\_}{}^{+1.17}-1.30$	1.30${}_{\_}{}^{+0.27}-0.24$	25	0.849	S	40.1$\pm$0.4
1097		23	38.0	38.2	17.4${}_{\_}{}^{+7.4}-5.6$	1.75${}_{\_}{}^{+0.20}-0.18$	25	0.261	28.9${}_{\_}{}^{+7.2}-6.3$	1.20∗	2.20∗	33	0.387	B	40.1$\pm$0.1
1291		62	37.1	37.3	9.26${}_{\_}{}^{+1.77}-1.58$	1.69${}_{\_}{}^{+0.11}-0.09$	36	0.162	21.5${}_{\_}{}^{+4.7}-4.1$	0.90${}_{\_}{}^{+0.19}-0.20$	2.60${}_{\_}{}^{+0.40}-0.31$	25	0.173	B	39.7${}_{\_}{}^{+0.2}-0.1$
1316		81	37.9	38.1	70.6${}_{\_}{}^{+14.6}-12.3$	2.21${}_{\_}{}^{+0.19}-0.16$	28	0.383	70.4${}_{\_}{}^{+15.8}-13.1$	1.20∗	2.20${}_{\_}{}^{+0.19}-0.17$	28	0.383	S	40.9${}_{\_}{}^{+0.2}-0.1$
1404		61	37.6	37.9	20.7${}_{\_}{}^{+3.3}-3.1$	1.99${}_{\_}{}^{+0.14}-0.12$	27	0.061	19.6${}_{\_}{}^{+4.3}-3.8$	2.09${}_{\_}{}^{+0.35}-0.34$	1.95${}_{\_}{}^{+0.20}-0.17$	27	0.047	S	40.4$\pm$0.1
2841		40	37.6	37.8	12.2${}_{\_}{}^{+2.9}-2.6$	2.05${}_{\_}{}^{+0.23}-0.19$	24	0.218	13.9${}_{\_}{}^{+4.2}-3.6$	1.70${}_{\_}{}^{+0.58}-0.59$	2.17${}_{\_}{}^{+0.34}-0.26$	24	0.283	S	40.2$\pm$0.1
3031	M81	185	35.9	36.3	5.15${}_{\_}{}^{+1.07}-0.93$	1.43$\pm$0.06	50	0.034	10.6${}_{\_}{}^{+2.7}-2.4$	1.18$\pm$0.09	2.16${}_{\_}{}^{+0.31}-0.25$	43	0.092	B	39.7${}_{\_}{}^{+0.3}-0.2$
3184		26	37.0	37.2	2.17${}_{\_}{}^{+0.87}-0.74$	1.56${}_{\_}{}^{+0.19}-0.17$	37	0.782	7.25${}_{\_}{}^{+3.29}-2.66$	0.35${}_{\_}{}^{+0.35}-0.24$	2.73${}_{\_}{}^{+0.87}-0.58$	34	0.773	B	39.2$\pm$0.3
3198		11	37.1	37.3	1.51${}_{\_}{}^{+0.74}-0.61$	1.45${}_{\_}{}^{+0.22}-0.19$	30	0.748	4.01${}_{\_}{}^{+2.37}-1.73$	0.28${}_{\_}{}^{+0.37}-0.20$	2.23${}_{\_}{}^{+0.92}-0.48$	28	0.851	B	39.2${}_{\_}{}^{+0.5}-0.4$
3351	M95	38	36.7	36.9	2.88${}_{\_}{}^{+0.89}-0.76$	1.59${}_{\_}{}^{+0.14}-0.12$	23	0.008	7.92${}_{\_}{}^{+3.24}-2.53$	0.93${}_{\_}{}^{+0.25}-0.27$	2.78${}_{\_}{}^{+0.87}-0.55$	21	0.032	B	39.3${}_{\_}{}^{+0.3}-0.2$
3521		51	37.2	37.4	9.05${}_{\_}{}^{+1.79}-1.60$	1.55$\pm$0.09	45	0.545	22.1${}_{\_}{}^{+4.7}-4.3$	0.36${}_{\_}{}^{+0.27}-0.22$	2.17${}_{\_}{}^{+0.23}-0.21$	30	0.267	B	40.0$\pm$0.2
3627	M66	61	37.1	37.3	8.43${}_{\_}{}^{+1.60}-1.46$	1.55$\pm$0.09	45	0.554	15.5${}_{\_}{}^{+3.7}-3.2$	0.98${}_{\_}{}^{+0.21}-0.22$	1.95${}_{\_}{}^{+0.20}-0.18$	41	0.738	B	40.1$\pm$0.2
3938		23	37.2	37.4	4.03${}_{\_}{}^{+1.24}-1.05$	1.65${}_{\_}{}^{+0.17}-0.16$	23	0.056	8.06${}_{\_}{}^{+3.24}-2.55$	0.76$\pm$0.42	2.23${}_{\_}{}^{+0.54}-0.35$	23	0.219	B	39.5$\pm$0.3
4125		35	37.7	37.9	15.8${}_{\_}{}^{+3.6}-3.3$	2.26${}_{\_}{}^{+0.29}-0.23$	26	0.458	20.9${}_{\_}{}^{+5.6}-4.9$	1.20∗	2.44${}_{\_}{}^{+0.53}-0.35$	28	0.796	S	40.3${}_{\_}{}^{+0.3}-0.1$
4254	M99	32	37.7	37.9	14.9${}_{\_}{}^{+3.8}-3.4$	2.02${}_{\_}{}^{+0.22}-0.19$	16	0.017	16.4${}_{\_}{}^{+4.7}-4.1$	1.60∗	2.08${}_{\_}{}^{+0.29}-0.24$	15	0.019	S	40.3$\pm$0.1
4321	M100	60	37.1	37.3	8.18${}_{\_}{}^{+1.70}-1.51$	1.53${}_{\_}{}^{+0.10}-0.09$	44	0.363	17.8${}_{\_}{}^{+4.3}-3.7$	0.71${}_{\_}{}^{+0.25}-0.26$	2.04${}_{\_}{}^{+0.24}-0.19$	36	0.399	B	40.1$\pm$0.2
4450		7	38.2	38.4	45.6${}_{\_}{}^{+63.0}-27.2$	3.47${}_{\_}{}^{+1.08}-0.89$	13	0.464	14.0${}_{\_}{}^{+6.5}-5.3$	1.20∗	2.20∗	12	0.148	B	39.8$\pm$0.2
4536		10	38.0	38.1	6.20${}_{\_}{}^{+4.41}-2.84$	1.76${}_{\_}{}^{+0.36}-0.28$	22	0.604	6.85${}_{\_}{}^{+4.94}-3.17$	1.60∗	1.83${}_{\_}{}^{+0.41}-0.30$	22	0.693	S	40.1${}_{\_}{}^{+0.3}-0.2$
4552	M89	115	37.2	37.6	23.3${}_{\_}{}^{+2.7}-2.6$	1.76${}_{\_}{}^{+0.08}-0.07$	40	0.002	34.9${}_{\_}{}^{+5.1}-4.7$	1.28$\pm$0.16	2.07${}_{\_}{}^{+0.15}-0.14$	35	0.068	B	40.3$\pm$0.1
4559		5	37.5	37.6	0.62${}_{\_}{}^{+0.66}-0.39$	1.17${}_{\_}{}^{+0.28}-0.27$	20	0.668	0.74${}_{\_}{}^{+0.80}-0.46$	0.90${}_{\_}{}^{+0.90}-0.61$	1.25${}_{\_}{}^{+0.32}-0.29$	20	0.768	S	40.1${}_{\_}{}^{+0.4}-0.5$
4569		26	37.7	37.8	8.85${}_{\_}{}^{+2.90}-2.50$	2.09${}_{\_}{}^{+0.29}-0.26$	20	0.132	12.1${}_{\_}{}^{+4.4}-3.7$	1.13${}_{\_}{}^{+0.78}-0.69$	2.46${}_{\_}{}^{+0.60}-0.39$	19	0.255	B	39.7${}_{\_}{}^{+0.3}-0.2$
4594	M104	192	36.8	37.1	21.3${}_{\_}{}^{+2.2}-2.1$	1.59$\pm$0.05	59	0.707	48.0${}_{\_}{}^{+5.5}-5.2$	1.06${}_{\_}{}^{+0.07}-0.08$	2.45${}_{\_}{}^{+0.20}-0.17$	22	0.010	B	40.2$\pm$0.1
4725		36	37.3	37.5	5.57${}_{\_}{}^{+1.60}-1.38$	1.72${}_{\_}{}^{+0.17}-0.15$	31	0.274	10.1${}_{\_}{}^{+3.8}-3.1$	1.01$\pm$0.38	2.32${}_{\_}{}^{+0.59}-0.36$	30	0.694	B	39.6${}_{\_}{}^{+0.3}-0.2$
4736	M94	71	36.5	36.8	4.97${}_{\_}{}^{+1.02}-0.88$	1.42${}_{\_}{}^{+0.08}-0.07$	55	0.554	8.82${}_{\_}{}^{+2.54}-2.09$	1.13${}_{\_}{}^{+0.13}-0.14$	1.81${}_{\_}{}^{+0.21}-0.18$	52	0.842	B	40.1$\pm$0.3
4826	M64	33	37.0	37.2	2.96${}_{\_}{}^{+1.05}-0.89$	1.51${}_{\_}{}^{+0.17}-0.14$	25	0.044	10.2${}_{\_}{}^{+3.6}-3.1$	0.29${}_{\_}{}^{+0.27}-0.20$	2.55${}_{\_}{}^{+0.60}-0.43$	17	0.023	B	39.4${}_{\_}{}^{+0.3}-0.2$
5033		24	37.7	37.9	12.5${}_{\_}{}^{+3.1}-2.8$	2.19${}_{\_}{}^{+0.27}-0.24$	30	0.884	16.3${}_{\_}{}^{+5.4}-4.5$	1.49$\pm$0.74	2.60${}_{\_}{}^{+0.91}-0.45$	31	0.424	B	39.8${}_{\_}{}^{+0.4}-0.2$
5055	M63	61	37.1	37.3	7.88${}_{\_}{}^{+1.60}-1.40$	1.59$\pm$0.10	34	0.101	12.6${}_{\_}{}^{+3.3}-2.8$	1.17${}_{\_}{}^{+0.21}-0.22$	1.91${}_{\_}{}^{+0.21}-0.18$	33	0.215	B	40.1$\pm$0.2
5194	M51	237	36.3	36.6	10.1${}_{\_}{}^{+1.5}-1.4$	1.59$\pm$0.05	49	0.034	11.4${}_{\_}{}^{+2.4}-2.1$	1.55$\pm$0.07	1.71${}_{\_}{}^{+0.15}-0.13$	48	0.062	B	40.4$\pm$0.2
5236	M83	363	35.9	36.2	8.94${}_{\_}{}^{+1.42}-1.31$	1.56${}_{\_}{}^{+0.05}-0.04$	57	0.073	12.0${}_{\_}{}^{+2.3}-2.1$	1.47${}_{\_}{}^{+0.06}-0.05$	1.93${}_{\_}{}^{+0.22}-0.18$	54	0.182	B	40.1$\pm$0.2
5457	M101	174	36.1	36.3	3.90${}_{\_}{}^{+1.07}-0.93$	1.62$\pm$0.08	38	0.019	6.14${}_{\_}{}^{+2.45}-1.86$	1.47${}_{\_}{}^{+0.12}-0.13$	2.41${}_{\_}{}^{+0.78}-0.45$	37	0.088	B	39.4${}_{\_}{}^{+0.3}-0.2$
5713		15	38.3	38.7	10.2${}_{\_}{}^{+10.0}-5.7$	1.49$\pm$0.24	29	0.456	13.9${}_{\_}{}^{+4.4}-3.8$	1.60∗	1.60∗	30	0.638	S	40.7$\pm$0.2
5866	M102	36	37.4	37.6	8.08${}_{\_}{}^{+1.95}-1.72$	1.95${}_{\_}{}^{+0.18}-0.17$	26	0.214	19.6${}_{\_}{}^{+5.1}-4.4$	0.64${}_{\_}{}^{+0.37}-0.34$	3.30${}_{\_}{}^{+0.69}-0.53$	17	0.188	B	39.5$\pm$0.1
6946		115	36.4	36.7	6.01${}_{\_}{}^{+1.23}-1.07$	1.49$\pm$0.07	53	0.289	8.99${}_{\_}{}^{+2.49}-2.08$	1.30${}_{\_}{}^{+0.12}-0.11$	1.78${}_{\_}{}^{+0.20}-0.18$	52	0.552	B	40.1$\pm$0.3
7331		95	37.2	37.5	18.3${}_{\_}{}^{+2.4}-2.3$	1.65${}_{\_}{}^{+0.08}-0.07$	56	0.710	28.7${}_{\_}{}^{+4.7}-4.3$	1.06${}_{\_}{}^{+0.19}-0.20$	1.92${}_{\_}{}^{+0.14}-0.13$	50	0.703	B	40.4$\pm$0.2
7552		14	37.4	37.6	2.95${}_{\_}{}^{+1.25}-0.98$	1.43${}_{\_}{}^{+0.19}-0.16$	28	0.190	4.72${}_{\_}{}^{+2.32}-1.70$	0.43${}_{\_}{}^{+0.50}-0.31$	1.67${}_{\_}{}^{+0.28}-0.23$	27	0.351	B	40.0${}_{\_}{}^{+0.3}-0.4$

Table 4. Table 4: Best Fit Parameters for Global Fits

Parameter		First	Second	Cleaned	Full	M12/Z12
Name	Units	Subsample	Subsample	Sample	Sample	Value
(1)	(2)	(3)	(4)	(5)	(6)	(7)
SFR	$M_{\odot }$ yr-1	18.5	26.9	40.9	45.4
$M_{\_}\star$	${10}^{11}$ $M_{\odot }$	7.97	4.50	10.21	12.47
$\log$ sSFR	$\log$ yr-1	$-$10.63	$-$10.22	$-$10.40	$-$10.44
$N_{\_}\det$		852	1626	2071	2478
Parameter Fit Values
$K_{\_}\mathrm{LMXB}$	(${10}^{11}$ $M_{\odot }$)-1	32.3${}_{\_}{}^{+5.7}-5.7$	39.6${}_{\_}{}^{+2.1}-2.0$	26.0${}_{\_}{}^{+3.4}-2.4$	33.8${}_{\_}{}^{+7.3}-3.6$	$41.5\pm 11.5$
${\alpha }_{\_}1$		1.21${}_{\_}{}^{+0.08}-0.08$	1.31${}_{\_}{}^{+0.03}-0.04$	1.31${}_{\_}{}^{+0.05}-0.07$	1.28${}_{\_}{}^{+0.06}-0.09$	1.02${}_{\_}{}^{+0.07}-0.08$
$L_{\_}b$	${10}^{38}$ erg s-1	0.77${}_{\_}{}^{+0.39}-0.16$	3.27${}_{\_}{}^{+0.51}-0.55$	2.16${}_{\_}{}^{+1.39}-0.71$	1.48${}_{\_}{}^{+0.70}-0.66$	${0.546}_{\_}^{+0.043}-0.037$
${\alpha }_{\_}2$		2.15${}_{\_}{}^{+0.15}-0.11$	3.15${}_{\_}{}^{+0.56}-0.42$	2.57${}_{\_}{}^{+0.54}-0.28$	2.33${}_{\_}{}^{+0.27}-0.21$	2.06${}_{\_}{}^{+0.06}-0.05$
$L_{\_}b,2^{†}$	${10}^{38}$ erg s-1					${5.99}_{\_}^{+0.95}-0.67$
${\alpha }_{\_}{3}^{†}$						${3.63}_{\_}^{+0.67}-0.49$
$K_{\_}\mathrm{HMXB}$	($M_{\odot }$ yr-1)-1	2.43${}_{\_}{}^{+0.27}-0.27$	1.48${}_{\_}{}^{+0.14}-0.14$	2.06${}_{\_}{}^{+0.16}-0.15$	1.96${}_{\_}{}^{+0.14}-0.14$	$2.68\pm 0.13$
$\gamma$		1.53${}_{\_}{}^{+0.05}-0.05$	1.71${}_{\_}{}^{+0.03}-0.03$	1.66${}_{\_}{}^{+0.02}-0.02$	1.65${}_{\_}{}^{+0.03}-0.02$	$1.58\pm 0.02$
$\log Lc$	$\log$ erg s-1	40.5${}_{\_}{}^{+0.4}-0.1$	41.0${}_{\_}{}^{+0.5}-0.3$	40.8${}_{\_}{}^{+0.5}-0.2$	40.7${}_{\_}{}^{+0.4}-0.2$	${40.04}_{\_}^{+0.18}-0.16$
$C$		1014	1185	1331	1410	…
$P_{\_}\mathrm{null}$		0.705	0.017	0.177	0.145	…
Calculated Parameters
$\log {\alpha }_{\_}\mathrm{LMXB}$	$\log$ erg s-1 $M_{\_}{\odot }^{-1}$	29.14${}_{\_}{}^{+0.07}-0.06$	29.31${}_{\_}{}^{+0.05}-0.04$	29.15${}_{\_}{}^{+0.07}-0.05$	29.25${}_{\_}{}^{+0.07}-0.06$	$29.2\pm 0.1$
$\log {\beta }_{\_}\mathrm{HMXB}$	$\log$ erg s-1 ($M_{\odot }$ yr-1)-1	39.89${}_{\_}{}^{+0.15}-0.11$	39.56${}_{\_}{}^{+0.15}-0.13$	39.73${}_{\_}{}^{+0.15}-0.10$	39.71${}_{\_}{}^{+0.14}-0.09$	$39.67\pm 0.06$

Table 5. Table 5: Global X-ray Luminosity Function Fits By Galaxy

Galaxy		Global Model					Scaled Global Model			Power-Law
Name	Alt
(NGC)	Name	$C$	$P_{\_}\mathrm{Null}$	$P\left(L_{\_}\mathrm{ps}\right)$	$P\left(N_{\_}38\right)$	$P\left(N_{\_}39\right)$	$\omega$	$C$	$P_{\_}\mathrm{Null}$	$C$	$P_{\_}{\mathrm{Null}}^{\mathrm{PL}}$	$C$	$P_{\_}{\mathrm{Null}}^{\mathrm{BKNPL}}$
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)
337		29	0.001	0.034	…	0.005	3.82${}_{\_}{}^{+1.57}-1.22$	23	0.440	22	0.944	23	0.889
584		9	0.899	0.719	…	0.189	1.68${}_{\_}{}^{+0.97}-0.71$	9	0.478	11	0.686	9	0.169
628	M74	32	0.543	0.720	0.852	0.360	1.52${}_{\_}{}^{+0.37}-0.32$	30	0.239	31	0.106	26	0.109
925		33	0.001	0.045	0.067	0.004	3.28${}_{\_}{}^{+1.44}-1.12$	30	0.067	26	0.785	25	0.849
1097		32	0.730	0.742	…	0.308	0.69${}_{\_}{}^{+0.17}-0.15$	29	0.814	25	0.261	33	0.387
1291		37	0.853	0.924	0.942	0.776	0.66${}_{\_}{}^{+0.10}-0.09$	27	0.389	36	0.162	25	0.173
1316		54	0.001	0.995	…	0.938	0.55$\pm$0.07	29	0.852	28	0.383	28	0.383
1404		36	0.517	0.715	0.930	0.385	0.77${}_{\_}{}^{+0.11}-0.10$	32	0.781	27	0.061	27	0.047
2841		25	0.630	0.774	0.724	0.781	0.82${}_{\_}{}^{+0.17}-0.15$	24	0.585	24	0.218	24	0.283
3031	M81	44	0.503	0.362	0.567	0.206	0.90$\pm$0.12	43	0.486	50	0.034	43	0.092
3184		35	0.527	0.428	0.049	0.440	1.20${}_{\_}{}^{+0.38}-0.33$	35	0.670	37	0.782	34	0.773
3198		31	0.639	0.392	0.230	0.139	0.74${}_{\_}{}^{+0.30}-0.25$	30	0.477	30	0.748	28	0.851
3351	M95	20	0.035	0.609	0.471	0.507	1.03${}_{\_}{}^{+0.23}-0.20$	20	0.034	23	0.008	21	0.032
3521		39	0.642	0.386	0.091	0.494	1.04${}_{\_}{}^{+0.17}-0.15$	39	0.666	45	0.545	30	0.267
3627	M66	44	0.498	0.221	0.215	0.282	1.04${}_{\_}{}^{+0.16}-0.14$	44	0.516	45	0.554	41	0.738
3938		27	0.790	0.294	0.118	0.470	1.96${}_{\_}{}^{+0.50}-0.43$	23	0.244	23	0.056	23	0.219
4125		33	0.511	0.506	0.949	0.498	0.69${}_{\_}{}^{+0.14}-0.12$	29	0.794	26	0.458	28	0.796
4254	M99	16	0.036	0.823	0.287	0.917	1.13${}_{\_}{}^{+0.25}-0.22$	16	0.027	16	0.017	15	0.019
4321	M100	42	0.697	0.497	0.073	0.563	1.03${}_{\_}{}^{+0.17}-0.15$	42	0.712	44	0.363	36	0.399
4450		12	0.485	0.823	…	0.548	1.18${}_{\_}{}^{+0.54}-0.42$	12	0.399	13	0.464	12	0.148
4536		23	0.953	0.568	…	0.254	0.83${}_{\_}{}^{+0.32}-0.25$	23	0.819	22	0.604	22	0.693
4552	M89	99	0.001	0.062	0.001	0.603	2.83${}_{\_}{}^{+0.29}-0.27$	32	0.675	40	0.002	35	0.068
4559		26	0.203	0.053	0.455	0.017	0.82${}_{\_}{}^{+0.54}-0.39$	25	0.142	20	0.668	20	0.768
4569		20	0.280	0.860	0.703	0.771	0.77${}_{\_}{}^{+0.21}-0.18$	19	0.259	20	0.132	19	0.255
4594	M104	40	0.944	0.401	0.234	0.814	1.39${}_{\_}{}^{+0.11}-0.10$	26	0.071	59	0.707	22	0.010
4725		30	0.938	0.495	0.687	0.591	0.91${}_{\_}{}^{+0.21}-0.18$	30	0.952	31	0.274	30	0.694
4736	M94	57	0.077	0.165	0.089	0.047	1.15${}_{\_}{}^{+0.18}-0.16$	57	0.115	55	0.554	52	0.842
4826	M64	31	0.672	0.861	0.672	0.613	0.49${}_{\_}{}^{+0.13}-0.12$	20	0.143	25	0.044	17	0.023
5033		33	0.226	0.339	0.513	0.124	1.31${}_{\_}{}^{+0.30}-0.25$	32	0.453	30	0.884	31	0.424
5055	M63	35	0.988	0.376	0.043	0.682	1.33${}_{\_}{}^{+0.21}-0.19$	33	0.637	34	0.101	33	0.215
5194	M51	53	0.895	0.427	0.319	0.215	1.18${}_{\_}{}^{+0.10}-0.09$	50	0.751	49	0.034	48	0.062
5236	M83	52	0.650	0.597	0.274	0.652	0.95$\pm$0.07	51	0.635	57	0.073	54	0.182
5457	M101	38	0.288	0.553	0.373	0.649	1.18${}_{\_}{}^{+0.17}-0.15$	37	0.207	38	0.019	37	0.088
5713		32	0.142	0.135	…	0.167	1.20${}_{\_}{}^{+0.37}-0.30$	32	0.259	29	0.456	30	0.638
5866	M102	21	0.322	0.810	0.492	0.562	1.13${}_{\_}{}^{+0.23}-0.20$	21	0.282	26	0.214	17	0.188
6946		60	0.237	0.481	0.271	0.602	0.74$\pm$0.10	54	0.415	53	0.289	52	0.552
7331		50	0.117	0.216	0.137	0.518	1.04${}_{\_}{}^{+0.12}-0.11$	50	0.126	56	0.710	50	0.703
7552		47	0.148	0.803	0.934	0.519	0.36${}_{\_}{}^{+0.12}-0.10$	30	0.803	28	0.190	27	0.351

Table 6. Table 6: Expected Statistical Scatter For Global Model

	$\log M_{\_}\star /M_{\_}\odot$
	(9.0)	(9.5)	(10.0)	(10.5)	(11.0)	(11.5)
$\log$ sSFR	$\log L_{\_}X$	$\log L_{\_}X$	$\log L_{\_}X$	$\log L_{\_}X$	$\log L_{\_}X$	$\log L_{\_}X$
(yr-1)	(erg s-1)	(erg s-1)	(erg s-1)	(erg s-1)	(erg s-1)	(erg s-1)
$-$12.5	37.86${}_{\_}{}^{}-{0.57}^{+0.76}$	38.53${}_{\_}{}^{}-{0.38}^{+0.44}$	39.13${}_{\_}{}^{}-{0.28}^{+0.27}$	39.68${}_{\_}{}^{}-{0.22}^{+0.19}$	40.22${}_{\_}{}^{}-{0.17}^{+0.15}$	40.74${}_{\_}{}^{}-{0.14}^{+0.13}$
$-$12.3	37.86${}_{\_}{}^{}-{0.58}^{+0.75}$	38.53${}_{\_}{}^{}-{0.39}^{+0.44}$	39.13${}_{\_}{}^{}-{0.28}^{+0.27}$	39.68${}_{\_}{}^{}-{0.22}^{+0.20}$	40.22${}_{\_}{}^{}-{0.17}^{+0.15}$	40.74${}_{\_}{}^{}-{0.14}^{+0.13}$
$-$12.1	37.86${}_{\_}{}^{}-{0.58}^{+0.76}$	38.53${}_{\_}{}^{}-{0.39}^{+0.44}$	39.13${}_{\_}{}^{}-{0.28}^{+0.27}$	39.69${}_{\_}{}^{}-{0.22}^{+0.19}$	40.22${}_{\_}{}^{}-{0.17}^{+0.16}$	40.75${}_{\_}{}^{}-{0.14}^{+0.13}$
$-$11.9	37.86${}_{\_}{}^{}-{0.58}^{+0.75}$	38.54${}_{\_}{}^{}-{0.39}^{+0.44}$	39.13${}_{\_}{}^{}-{0.28}^{+0.27}$	39.69${}_{\_}{}^{}-{0.22}^{+0.19}$	40.23${}_{\_}{}^{}-{0.17}^{+0.15}$	40.75${}_{\_}{}^{}-{0.14}^{+0.13}$
$-$11.7	37.88${}_{\_}{}^{}-{0.57}^{+0.76}$	38.54${}_{\_}{}^{}-{0.39}^{+0.43}$	39.14${}_{\_}{}^{}-{0.29}^{+0.27}$	39.70${}_{\_}{}^{}-{0.22}^{+0.20}$	40.24${}_{\_}{}^{}-{0.18}^{+0.16}$	40.76${}_{\_}{}^{}-{0.14}^{+0.13}$
$-$11.4	37.88${}_{\_}{}^{}-{0.57}^{+0.75}$	38.55${}_{\_}{}^{}-{0.39}^{+0.43}$	39.14${}_{\_}{}^{}-{0.29}^{+0.27}$	39.71${}_{\_}{}^{}-{0.23}^{+0.19}$	40.25${}_{\_}{}^{}-{0.18}^{+0.16}$	40.78${}_{\_}{}^{}-{0.14}^{+0.13}$
$-$11.2	37.89${}_{\_}{}^{}-{0.58}^{+0.75}$	38.56${}_{\_}{}^{}-{0.39}^{+0.43}$	39.16${}_{\_}{}^{}-{0.29}^{+0.27}$	39.72${}_{\_}{}^{}-{0.23}^{+0.19}$	40.27${}_{\_}{}^{}-{0.19}^{+0.16}$	40.80${}_{\_}{}^{}-{0.14}^{+0.13}$
$-$11.0	37.90${}_{\_}{}^{}-{0.57}^{+0.73}$	38.58${}_{\_}{}^{}-{0.39}^{+0.42}$	39.18${}_{\_}{}^{}-{0.30}^{+0.26}$	39.75${}_{\_}{}^{}-{0.24}^{+0.20}$	40.30${}_{\_}{}^{}-{0.20}^{+0.16}$	40.84${}_{\_}{}^{}-{0.15}^{+0.14}$
$-$10.8	37.93${}_{\_}{}^{}-{0.57}^{+0.72}$	38.61${}_{\_}{}^{}-{0.40}^{+0.41}$	39.22${}_{\_}{}^{}-{0.31}^{+0.27}$	39.79${}_{\_}{}^{}-{0.27}^{+0.20}$	40.35${}_{\_}{}^{}-{0.22}^{+0.17}$	40.89${}_{\_}{}^{}-{0.15}^{+0.14}$
$-$10.6	37.97${}_{\_}{}^{}-{0.56}^{+0.68}$	38.66${}_{\_}{}^{}-{0.41}^{+0.40}$	39.27${}_{\_}{}^{}-{0.34}^{+0.27}$	39.85${}_{\_}{}^{}-{0.30}^{+0.21}$	40.43${}_{\_}{}^{}-{0.23}^{+0.18}$	40.97${}_{\_}{}^{}-{0.15}^{+0.14}$
$-$10.4	38.04${}_{\_}{}^{}-{0.56}^{+0.64}$	38.72${}_{\_}{}^{}-{0.42}^{+0.38}$	39.34${}_{\_}{}^{}-{0.37}^{+0.27}$	39.95${}_{\_}{}^{}-{0.33}^{+0.22}$	40.53${}_{\_}{}^{}-{0.24}^{+0.19}$	41.07${}_{\_}{}^{}-{0.14}^{+0.15}$
$-$10.2	38.14${}_{\_}{}^{}-{0.56}^{+0.59}$	38.82${}_{\_}{}^{}-{0.45}^{+0.37}$	39.45${}_{\_}{}^{}-{0.41}^{+0.28}$	40.07${}_{\_}{}^{}-{0.35}^{+0.24}$	40.67${}_{\_}{}^{}-{0.22}^{+0.20}$	41.20${}_{\_}{}^{}-{0.14}^{+0.15}$
$-$10.0	38.27${}_{\_}{}^{}-{0.55}^{+0.53}$	38.96${}_{\_}{}^{}-{0.49}^{+0.35}$	39.61${}_{\_}{}^{}-{0.44}^{+0.29}$	40.25${}_{\_}{}^{}-{0.34}^{+0.26}$	40.83${}_{\_}{}^{}-{0.20}^{+0.21}$	41.35$\pm$0.14
$-$9.8	38.44${}_{\_}{}^{}-{0.57}^{+0.48}$	39.13${}_{\_}{}^{}-{0.52}^{+0.35}$	39.81${}_{\_}{}^{}-{0.46}^{+0.32}$	40.45${}_{\_}{}^{}-{0.30}^{+0.28}$	41.01${}_{\_}{}^{}-{0.18}^{+0.20}$	41.52$\pm$0.14
$-$9.6	38.65${}_{\_}{}^{}-{0.60}^{+0.44}$	39.35${}_{\_}{}^{}-{0.55}^{+0.37}$	40.04${}_{\_}{}^{}-{0.42}^{+0.33}$	40.66${}_{\_}{}^{}-{0.25}^{+0.27}$	41.20${}_{\_}{}^{}-{0.16}^{+0.18}$	41.70${}_{\_}{}^{}-{0.13}^{+0.14}$
$-$9.3	38.89${}_{\_}{}^{}-{0.61}^{+0.43}$	39.61${}_{\_}{}^{}-{0.53}^{+0.38}$	40.28${}_{\_}{}^{}-{0.37}^{+0.33}$	40.87${}_{\_}{}^{}-{0.21}^{+0.24}$	41.39${}_{\_}{}^{}-{0.15}^{+0.17}$	41.89${}_{\_}{}^{}-{0.13}^{+0.14}$
$-$9.1	39.16${}_{\_}{}^{}-{0.60}^{+0.42}$	39.88${}_{\_}{}^{}-{0.48}^{+0.38}$	40.53${}_{\_}{}^{}-{0.29}^{+0.31}$	41.08${}_{\_}{}^{}-{0.18}^{+0.21}$	41.59${}_{\_}{}^{}-{0.14}^{+0.15}$	42.09$\pm$0.13
$-$8.9	39.45${}_{\_}{}^{}-{0.58}^{+0.42}$	40.15${}_{\_}{}^{}-{0.41}^{+0.37}$	40.77${}_{\_}{}^{}-{0.23}^{+0.28}$	41.29${}_{\_}{}^{}-{0.16}^{+0.19}$	41.79${}_{\_}{}^{}-{0.14}^{+0.15}$	42.29$\pm$0.13
$-$8.7	39.75${}_{\_}{}^{}-{0.52}^{+0.41}$	40.42${}_{\_}{}^{}-{0.33}^{+0.34}$	40.98${}_{\_}{}^{}-{0.20}^{+0.23}$	41.50${}_{\_}{}^{}-{0.15}^{+0.17}$	42.00${}_{\_}{}^{}-{0.13}^{+0.14}$	42.50$\pm$0.13
$-$8.5	40.04${}_{\_}{}^{}-{0.45}^{+0.39}$	40.67${}_{\_}{}^{}-{0.26}^{+0.30}$	41.20${}_{\_}{}^{}-{0.17}^{+0.20}$	41.71${}_{\_}{}^{}-{0.14}^{+0.15}$	42.21${}_{\_}{}^{}-{0.13}^{+0.14}$	42.71$\pm$0.13

Table 7. Table A1: X-ray point-source catalog and properties

		${\alpha }_{\_}\mathrm{J2000}$	${\delta }_{\_}\mathrm{J2000}$	$\theta$	$N_{\_}\mathrm{FB}$	$N_{\_}H$		$\log F_{\_}\mathrm{FB}$	$\log L_{\_}\mathrm{FB}$	Location
Galaxy	ID	(deg)	(deg)	(arcmin)	(counts)	(${10}^{22}$ cm-2)	$\Gamma$	(erg cm-2 s-1)	(erg s-1)	Flag
(1)	(2)	(3)	(4)	(5)	(6)–(7)	(8)–(9)	(10)–(11)	(12)	(13)	(14)
NGC337	1	00 59 43.53	$-$07 35 01.33	1.7	7.8$\pm$4.2	0.056	1.7	$-$14.1	38.6	4
	2	00 59 47.50	$-$07 34 16.68	0.8	41.0$\pm$7.9	0.109$\pm$0.154	3.06	$-$13.7	39.1	2
	3	00 59 48.51	$-$07 34 56.71	0.5	65.3$\pm$9.7	0.314$\pm$0.381	1.98$\pm$0.74	$-$13.2	39.5	1
	4	00 59 49.48	$-$07 34 35.66	0.2	106.8$\pm$12.1	0.308$\pm$0.326	1.60$\pm$0.53	$-$13.0	39.8	1
	5	00 59 49.49	$-$07 35 23.53	0.7	22.3$\pm$6.2	0.779$\pm$0.410	3.06	$-$13.8	38.9	2
	6	00 59 50.40	$-$07 34 45.67	0.1	4.7$\pm$2.2	0.056	1.7	$-$14.3	38.5	1
	7	00 59 50.40	$-$07 34 54.18	0.2	42.8$\pm$8.1	0.647$\pm$0.796	1.57$\pm$0.90	$-$13.3	39.5	1
	8	00 59 50.56	$-$07 34 58.08	0.3	300.5$\pm$19.5	0.136$\pm$0.155	1.40$\pm$0.29	$-$12.5	40.3	1
	9	00 59 51.90	$-$07 34 57.71	0.5	14.4$\pm$5.2	0.056	1.7	$-$13.8	39.0	1
	10	00 59 52.29	$-$07 34 47.38	0.6	43.3$\pm$8.1	0.405$\pm$0.510	2.17$\pm$0.97	$-$13.4	39.3	2
	11	00 59 53.31	$-$07 34 56.49	0.8	4.9$\pm$2.2	0.056	1.7	$-$14.3	38.5	2
	12	00 59 53.32	$-$07 35 20.76	1.0	27.3$\pm$6.7	0.477$\pm$0.787	1.67$\pm$1.12	$-$13.5	39.2	2
NGC584	1	01 31 09.45	$-$06 54 34.08	3.7	12.1$\pm$4.9	0.036	1.7	$-$13.8	38.9	4
	2	01 31 17.83	$-$06 54 34.75	2.6	5.9$\pm$2.4	0.036	1.7	$-$14.1	38.6	4
	3	01 31 18.02	$-$06 51 48.29	0.7	8.8$\pm$4.4	0.036	1.7	$-$13.8	38.9	1
	4	01 31 18.73	$-$06 52 06.49	0.5	1.9$\pm$1.4	0.036	1.7	$-$14.5	38.1	1
	5	01 31 19.28	$-$06 51 50.26	0.4	3.9$\pm$2.0	0.036	1.7	$-$14.2	38.4	1
	6	01 31 19.54	$-$06 52 03.87	0.3	2.9$\pm$1.7	0.036	1.7	$-$14.4	38.3	1
	7	01 31 20.00	$-$06 52 07.07	0.2	19.6$\pm$5.9	0.036	1.7	$-$13.6	39.1	1
	8	01 31 20.14	$-$06 51 41.03	0.4	3.9$\pm$2.0	0.036	1.7	$-$13.9	38.8	1

Equations

$$\left(\frac{\mathrm{SFR}}{M_{\_}\odot {\mathrm{yr}}^{-1}}\right)=1.6\times 10^{-10}\left[\left(\frac{L_{\_}{\mathrm{FUV}}^{\mathrm{obs}}}{L_{\_}\odot }\right)+3.89\left(\frac{L_{\_}{24\mu \mathrm{m}}^{\mathrm{obs}}}{L_{\_}\odot }\right)\right],$$

$$\log (M_{\_}\star /M_{\_}\odot )=\log (L_{\_}K/L_{\_}K,\odot )-1.321+0.754(g-i),$$

$$\log (M_{\_}\star /M_{\_}\odot )=\log (L_{\_}K/L_{\_}K,\odot )-1.390+1.176(B-V).$$

$$\frac{dN}{dL}=K_{\_}{\rm PL}\left\{\begin{array}[]{lr}L^{-\alpha},&\;\;\;\;\;\;\;\;(L<L_{\_}c)\\ 0,&(L\geq L_{\_}c)\end{array}\right.$$

$$\frac{dN}{dL}=K_{\_}{\rm BKNPL}\left\{\begin{array}[]{lr}L^{-\alpha_{\_}1}&\;\;\;\;\;\;\;\;(L<L_{\_}b)\\ L_{\_}b^{\alpha_{\_}2-\alpha_{\_}1}L^{-\alpha_{\_}2},&(L_{\_}b\leq L<L_{\_}c)\\ 0,&(L\geq L_{\_}c)\\ \end{array}\right.$$

$$\xi (L)=\sum _{\_}i{\xi }_{\_}i(L)\times w_{\_}i,$$

$$dN/dL(\mathrm{obs})=\xi (L)[dN/dL(\mathrm{int})+dN/dL(\mathrm{CXB})].$$

$$C=2\sum _{\_}{i=1}^n{M}_{\_}i-N_{\_}i+N_{\_}i\ln (N_{\_}i/M_{\_}i),$$

$$L_{\_}\mathrm{X}\equiv {\int }_{\_}{L_{\_}\mathrm{lo}}^{L_{\_}c}\frac{dN}{dL}LdL,$$

$$\frac{dN}{dL}=\xi (L)\left[\frac{d{N}_{\_}\mathrm{LMXB}}{dL}+\frac{d{N}_{\_}\mathrm{HMXB}}{dL}+\mathrm{CXB}\right]$$

$$\frac{dN_{\_}{\rm HMXB}}{dL}={\rm SFR}\;K_{\_}{\rm HMXB}\left\{\begin{array}[]{lr}L^{-\gamma}&\;\;\;\;\;\;\;\;(L<L_{\_}c)\\ 0,&(L\geq L_{\_}c)\\ \end{array}\right.$$

$$\frac{dN_{\_}{\rm LMXB}}{dL}=M_{\_}\star\;K_{\_}{\rm LMXB}\left\{\begin{array}[]{lr}L^{-\alpha_{\_}1}&\;\;\;\;\;\;\;\;(L<L_{\_}b)\\ L_{\_}b^{\alpha_{\_}2-\alpha_{\_}1}L^{-\alpha_{\_}2},&(L_{\_}b\leq L<L_{\_}c)\\ 0,&(L\geq L_{\_}c)\\ \end{array}\right.$$

$$C=2\sum _{\_}{i=1}^{n_{\_}\mathrm{sSFR}}\left(\sum _{\_}{j=1}^{n_{\_}\mathrm{X}}{M}_{\_}i,j-N_{\_}i,j+N_{\_}i,j\ln (N_{\_}i,j/M_{\_}i,j)\right),$$

$${\beta }_{\_}\mathrm{HMXB}\equiv \frac{1}{\mathrm{SFR}}{\int }_{\_}{L_{\_}\mathrm{lo}}^{L_{\_}\mathrm{c}}\frac{d{N}_{\_}\mathrm{HMXB}}{dL}LdL=L_{\_}\mathrm{X}(\mathrm{HMXB})/\mathrm{SFR}$$

$${\alpha }_{\_}\mathrm{LMXB}\equiv \frac{1}{M_{\_}\star }{\int }_{\_}{L_{\_}\mathrm{lo}}^{L_{\_}\mathrm{c}}\frac{d{N}_{\_}\mathrm{LMXB}}{dL}LdL=L_{\_}\mathrm{X}(\mathrm{LMXB})/M_{\_}\star ,$$

$$\frac{dN_{\_}{\rm XRB}}{dL}\biggr{\rvert}_{\_}{\rm scaled}=\omega\left(\frac{dN_{\_}{\rm LMXB}}{dL}+\frac{dN_{\_}{\rm HMXB}}{dL}\right).$$

$$S_{\_}N\equiv N_{\_}\mathrm{GC}\times 10^{0.4(M_{\_}{V}^T+15)},$$

Full text

stars: formation — galaxies: normal — X-rays: binaries — X-rays: galaxies

††software: ACIS Extract (v2016sep22; Broos et al. 2010, 2012), MARX (v5.3.2; Davis et al. 2012), CIAO (v4.8; Fruscione et al. 2006), xspec (v12.9.1; Arnaud 1996)

1 Introduction

X-ray binaries (XRBs) provide a direct probe of compact object (i.e., black hole [BH] and neutron star [NS]) populations and close binary systems in galaxies. The XRB phase of close-binary evolution results when mass is transferred from a normal star (secondary) to an accreting compact-object remnant (primary), via Roche-lobe overflow or stellar-wind mass transfer. Depending on the binary parameters, subsequent evolution beyond the XRB phase is expected to result in a variety of astrophysical systems, including, e.g., gravitational wave (GW) mergers, millisecond pulsars, and short gamma-ray bursts (GRBs). Recent discoveries of gravitational waves (GWs) from merging BHs and NSs from LIGO (e.g., Abbott et al. 2016, 2017) have prompted a resurgence in efforts to self-consistently model close binary populations and their evolution (e.g., Belczynski et al. 2016, 2018; Mandel & de Mink 2016; Marchant et al. 2017; Kruckow et al. 2018; Mapelli & Giacobbo 2018). As such, statistically meaningful constraints on XRB populations are critical to such efforts.

Thanks largely to data collected over the last two decades by Chandra and XMM-Newton, substantial insight has been gained into how the XRB phase is manifested within a variety of galactic environments beyond the Milky Way and Magellanic Clouds. Several studies of XRB emission from galaxies in the nearby Universe (D\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}50 Mpc) have established that the X-ray luminosity functions (XLFs), and population-integrated luminosities of high-mass XRBs (HMXBs) and low-mass XRBs (LMXBs) scale with star-formation rate (SFR) and stellar mass ($M_{\_}\star$), respectively (e.g., Grimm et al. 2003; Ranalli et al. 2003; Colbert et al. 2004; Gilfanov 2004; Lehmer et al. 2010; Boroson et al. 2011; Mineo et al. 2012a, 2012b, Zhang et al. 2012). These scaling relations have been assumed to be “universal” in applications outside of studies focused on XRBs. For example, studies of distant active galactic nuclei (AGN) routinely utilize local scaling relations when assessing the levels of XRB emission in distant populations. (see, e.g., $\S$2.2 of Hickox & Alexander 2018).

However, more recently, it has been suggested that the scatter in basic XRB scaling relations is larger than expected if the correlations were universal. XRB population synthesis models have indicated that universal scaling relations are unrealistic on physical grounds (e.g., Fragos et al. 2008, 2013a, 2013b; Zuo et al. 2014). For example, the population synthesis models from Fragos et al. (2013b) predict order-of-magnitude variations of $L_{\_}{\rm X}$(HMXB)/SFR and $L_{\_}{\rm X}$(LMXB)/$M_{\_}\star$ with metallicity and stellar age, respectively, over ranges of these quantities present in the observable Universe.

Since the ranges of metallicities and mean stellar ages for typical galaxies in the local Universe are relatively narrow, empirically measuring the predicted deviations of the scaling relations with these parameters has been challenging. Nonetheless, targeted observations of relatively rare, low metallicity late-type galaxies (e.g., Basu-Zych et al. 2013a, 2016; Douna et al. 2015; Brorby et al. 2016; Tzanavaris et al. 2016) and early-type galaxies with a range of stellar ages (e.g., Kim & Fabbiano 2010; Lehmer et al. 2014), have provided tantalizing evidence of variations in the scaling relations in line with those predicted by population synthesis models. New studies of XRB formation rates within very nearby galaxies (e.g., Magellanic Clouds, M33, M51, NGC 3310, and NGC 2276) have revealed similar variations with physical properties on subgalactic scales (e.g., Antoniou & Zezas 2016; Lehmer et al. 2017; Garofali et al. 2018; Anastasopoulou et al. 2018; Antoniou et al. 2019). Furthermore, X-ray stacking analyses of distant galaxy populations in deep Chandra surveys (e.g., the Chandra Deep Fields and Chandra COSMOS surveys) have claimed that there is redshift evolution in the scaling relations, potentially due to the corresponding decline in mean stellar population age and metallicity with lookback time (e.g., Lehmer et al. 2007, 2016; Basu-Zych et al. 2013b; Kaaret 2014; Aird et al. 2017).

The measured evolution of $L_{\_}{\rm X}$(HMXB)/SFR $\propto(1+z)$ and $L_{\_}{\rm X}$(LMXB)/$M_{\_}\star$ $\propto(1+z)^{2-3}$ out to $z\approx$ 2–4 (Lehmer et al. 2016; Aird et al. 2017) is only loosely constrained, but consistent with the population synthesis predictions from Fragos et al. (2013a); however, see Fornasini et al. (2018) for caveats. Extrapolation of the theoretical predictions into the very early Universe at z\lower 2.15277pt\hbox{;\buildrel>\over{\sim};}10, when the Universe was of very low metallicity ($\;\buildrel<\over{\sim}\;$1/10 $Z_{\_}\odot$; e.g., based on the Millenium II simulations; Guo et al. 2011), indicate that XRBs were likely the most luminous X-ray emitting population in the Universe (e.g., Fragos et al. 2013b; Lehmer et al. 2016; Madau & Fragos 2017). In fact, emission from XRBs is thought to play a dominant role in heating the IGM at $z\approx$ 10–20 (e.g., Mirabel et al. 2011; Mesinger et al. 2013; Pacucci et al. 2014; Das et al. 2017; Grieg & Mesinger 2018).

The studies outlined above indicate that XRBs play an important role in a variety of astrophysical systems and that the XRB scaling relations have non-negligible dependencies on galaxy physical properties. Although we now have some indications of how the XRB emission and scaling relations vary with important physical properties, there is still large uncertainty in how the distributions of XRB populations (i.e., XLFs) vary with these physical properties. In particular, we do not know precisely how the XRB XLFs vary with age and metallicity. There are some indications that the HMXB XLF in low-metallicity galaxies contains an excess of ultraluminous X-ray sources (ULXs) above $10^{39}$ erg s*-1* (Mapelli et al. 2010; Kaaret et al. 201; Prestwich et al. 2013; Basu-Zych et al. 2016) and the bright-end of the LMXB XLF for young elliptical galaxies contains more LMXBs with \;\buildrel>\over{\sim}\;$$10^{39} erg s*-1* than older ellipticals (e.g., Kim & Fabbiano 2010; Lehmer et al. 2014, 2017). But for both HMXBs and LMXBs, it is not clear whether there is an excess of XRBs over the full range of luminosities that are important to the galaxy-wide global X-ray power output, and to what extent these populations are elevated (due to small number statistics). These details are powerful constraints for population synthesis models, as they provide several additional degrees of freedom for modeling XRB populations, beyond scalings with integrated $L_{\_}{\rm X}$.

The most recent large-scale measurements of the XRB XLFs and their scalings with galaxy properties have employed a strategy of selecting galaxy samples with high specific-SFR (sSFR $\equiv$ SFR/$M_{\_}\star$) to isolate HMXB populations (Mineo et al. 2012, hereafter, M12; Sazonov & Khabibullin 2017a, 2017b) and elliptical galaxy populations that lack HMXBs to isolate LMXB populations (Zhang et al. 2012; hereafter, Z12; Peacock et al. 2017). By design, such a strategy excludes data from more representative populations of galaxies that are likely to have a mix of populations and has the potential to yield misleading results for a number of physical reasons. For example, late-type galaxies generally have younger mean stellar ages, and could have larger contributions from LMXBs than elliptical galaxies, since the LMXB emission per unit mass is expected to decline with increasing age (e.g., Fragos et al. 2008). Similarly, massive elliptical galaxies, which dominate studies of LMXB scaling relations, tend to have larger numbers of globular clusters (GCs) per unit mass than lower-mass late-type galaxies (e.g., Brodie & Strader 2006). GCs very efficiently produce LMXBs through dynamical interactions (Clark 1975; Fabian et al. 1975; Sivakoff et al. 2007; Cheng et al. 2018a, 2018b) and can even dominate the LMXB population of massive ellipticals (e.g., Irwin 2005; Kim et al. 2009; Voss et al. 2009; Lehmer et al. 2014) and produce XLFs that are different in shape to those of the LMXB population found in the galactic field.

In this paper, we delve into the Chandra archive of local (D\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}30 Mpc) galaxies to establish XRB XLF correlations with physical properties that are representative of the local galaxy population that makes up most of the mass of the local Universe (e.g., Blanton & Moustakas 2009). We make use of 5.8 Ms of Chandra ACIS imaging data across 38 galaxies to simultaneously constrain the HMXB and LMXB XLF shapes and scalings with SFR and $M_{\_}\star$, respectively. We employ a galaxy decomposition technique, developed in Lehmer et al. (2017), to statistically extract the contributions from HMXBs, LMXBs, and unrelated background sources (e.g., AGN and Galactic stars). This technique uses spatially-resolved maps of SFR and $M_{\_}\star$ for the galaxies in our sample to extract XRB population statistics from a range of local specific-SFRs, and then self-consistently models the XRB XLFs across the entire sSFR range.

Our goal here is to establish a baseline XLF model, for which we can compare observed XLFs of other galaxies and identify outliers to study in more detail. Furthermore, in subsequent studies, we will expand our sample and will investigate quantitatively how metallicity, stellar age, and GC populations influence the XRB XLFs. Our paper is organized as follows. In $\S$2, we discuss the galaxy sample selection. In $\S$3 we outline our analysis procedures for constructing maps of SFR and $M_{\_}\star$, as well as our detailed X-ray data reduction and point-source cataloging procedure. In $\S$4, we present the XLFs for our galaxies and culled regions selected by sSFR, and provide model fits to the XLFs. In $\S$5, we make comparisons of our HMXB and LMXB XLFs with past observational estimates and XRB population synthesis models, identify interesting galaxies with XRB populations that are outliers to the average, and discuss possible physical trends that explain these deviations. We also characterize the galaxy-to-galaxy scatter of the integrated XRB luminosity implied by our XLFs. Finally, we summarize our results in $\S$6. Full catalogs of the Chandra sources, Chandra images, as well as our SFR and $M_{\_}\star$ maps, are provided publicly at https://lehmer.uark.edu/downloads/.

2 Galaxy Sample Selection and Properties

We started by selecting a sample of nearby galaxies with Chandra coverage, as well as far-UV–to–IR multiwavelength data that was sufficient for measuring accurate SFR and $M_{\_}\star$ values on subgalactic scales. To this end, we searched for galaxies in the Spitzer Infrared Nearby Galaxies Survey (SINGS; Kennicutt et al. 2003) that also contained Chandra ACIS imaging data in the archive. The SINGS sample itself contains 75 nearby ($\;\buildrel<\over{\sim}\;$30 Mpc) galaxies, which were selected to be diverse in properties, and well resolved and efficiently observed by Spitzer and other multiwavelength facilities (covering angular sizes of 5–15 arcmin). We first limited our search to galaxies with $B$-band absolute magnitudes of $M_{\_}B<-19$ mag (as provided by Moustakas et al. 2010), which includes galaxies that are $\approx$1 mag below the knee of the $B$-band luminosity function and are in the range of galaxies that dominate the stellar mass density of the local universe (e.g., Blanton et al. 2003). We further restricted our sample to galaxies with inclinations to our line of sight that are $\;\buildrel<\over{\sim}\;$70 deg. Inclination, $i$, was estimated as $\sin(i)=\sqrt{1-(b/a)^{2}}$, where $a$ and $b$ are the semi-major and semi-minor axes, as defined in the $K_{\_}s$-band by Jarrett et al. (2003). This criteria is motivated by the fact that extinction due to a thin disk rapidly increases for inclinations above this value (e.g., Tuffs et al. 2004). Since we are unable to accurately correct for intrinsic extinction for the point sources, and expect that this extinction could have substantial effects on the observed XLFs, we have elected to exclude these galaxies.

The above selection resulted in 45 SINGS galaxies, with 36 of them having sufficient Chandra data. In addition to these galaxies, we elected to add to our sample NGC 5236 (M83) and NGC 5474 (M101), both of which have properties consistent with those selected in the SINGS galaxy sample and also have outstanding X-ray coverage due to large Chandra campaigns (Kuntz & Snowden 2010; Long et al. 2014). We note that the overall selection of galaxies is driven by the presence of excellent multiwavelength data mainly available through SINGS. The SINGS sample has 80% Chandra completeness, with many of the galaxies being observed due to their SINGS coverage (e.g., via the XSINGS program; PI: L. Jenkins; Tzanavaris et al. 2013), suggesting that our sample is not significantly biased towards X-ray bright galaxies. In total, our final sample contains 38 nearby galaxies.

In Figure 1, we show cut-out optical images of the galaxy sample, and in Table 1 we summarize the basic properties of each galaxy. Here we are interested in XLF scaling relations with the basic properties: SFR and $M_{\_}\star$. Calculations of galaxy-wide SFR and $M_{\_}\star$ values for our sample are detailed in $\S$3.1 below, and in Figure 2$a$ we graphically show their values on the SFR–$M_{\_}\star$ plane. Our sample spans 2.5 dex in SFR and $M_{\_}\star$, and by design, these galaxies were chosen to be diverse and do not strictly follow the galaxy “main sequence” (e.g., Elbaz et al. 2007; Noeske et al. 2007; Karim et al. 2011; Whitaker et al. 2014).

Since we expect that the HMXB-to-LMXB ratio will be dependent on sSFR, this quantity is of particular interest. In Figure 2$b$, we show the distribution of galaxy-wide sSFR (i.e., total galaxy SFR/$M_{\_}\star$) values for the 38 galaxies in our sample. Past studies have shown that around sSFR $\approx 10^{-10}$ yr*-1* the relative X-ray luminosities from HMXBs and LMXBs is nearly equal, while at higher and lower sSFR values HMXBs and LMXBs, respectively, dominate the XRB population luminosities (see, e.g., Colbert et al. 2004; Lehmer et al. 2010; M12). Our galaxy sample contains 15 and 23 galaxies, respectively, above and below this threshold, with the most extreme cases being NGC 337 (sSFR $\approx 5\times 10^{-10}$ yr*-1*) and NGC 1404 (sSFR $\approx 10^{-12}$ yr*-1*). As we will show below, we can quantify the HMXB and LMXB contributions to the XLFs of all late-type galaxies based on a self-consistent “global” model of the HMXB and LMXB XLF scaling with SFR and $M_{\_}\star$, respectively.

3 Data Analysis and Products

3.1 Multiwavelength Tracer Maps

For each galaxy in our sample, we generated SFR and $M_{\_}\star$ maps, using multiwavelength tracers of these quantities. For SFR, we made use of FUV GALEX and 24 $\mu$m Spitzer maps, and for $M_{\_}\star$, we utilized $K$-band data from the Two Micron All Sky Survey (2MASS) combined with optical $g$ and $i$ band data from the Sloan Digital Sky Survey (SDSS), when available. In the absence of SDSS, we utilized $B$ and $V$ band data available from the SINGS collaboration,111https://irsa.ipac.caltech.edu/data/SPITZER/SINGS/doc/sings_fifth_delivery_v2.pdf which originated from either the Kitt Peak National Observatory (KPNO) or Cerro Tololo Inter-American Observatory (CTIO), or in the case of NGC 6946, we made use of $B$ and $V$ band data from Swift. Our data preparation procedure, including the identification and subtraction of foreground Galactic stars, background subtraction, and convolution techniques followed closely that outlined in $\S\S$2.1–2.4 of Eufrasio et al. (2017) with a few minor differences. All images were convolved to a common Gaussian point-spread function (PSF) with a 15 arcsec full-width at half maximum (FWHM), which is significantly larger than the 24$\mu$m PSF to comfortably remove all PSF features and produce a Gaussian PSF. The images were projected to a common pixel scale of 3 arcsec pixel*-1*. For a galaxy at 30 Mpc, just beyond the most distant galaxy in our sample, this pixel scale results in a physical size of 436 pc pixel*-1*.

To calculate SFRs, we made use of the Hao et al. (2011) relation (implied by their Table 3):

[TABLE]

where $L_{\_}{\rm FUV}^{\rm obs}$ and $L_{\_}{24~{}\mu{\rm m}}^{\rm obs}$ are the observed (i.e., corrected only for Galactic extinction and not intrinsic extinction) monochromatic luminosities (e.g., $\nu L_{\_}\nu$) at 1528 Å and 24 $\mu$m, respectively. For each pixel, values of $L_{\_}{\rm FUV}^{\rm obs}$ and $L_{\_}{24~{}\mu{\rm m}}^{\rm obs}$ are determined from the GALEX FUV and Spitzer 24 $\mu$m maps, respectively. In the case of NGC 7552, Herschel 70 $\mu$m data was used instead of the Spitzer 24$\mu$m data, due to strong PSF contributions from the 24$\mu$m-bright nuclear starburst at large galactocentric radii. For this galaxy, we converted $L_{\_}{70}^{\rm obs}$ to $L_{\_}{24}^{\rm obs}$, using scaling relations from Kennicutt & Evans (2012) and Galametz et al. (2013). These SFRs are based on an assumed constant star-formation history with duration of 100 Myr, a Kroupa (2001) initial mass function (IMF), and solar metallicity (i.e., $Z=0.02$). The calibration is reported to have a 1$\sigma$ uncertainty of 0.1 dex.

Stellar masses ($M_{\_}\star$) were computed following the relations in Zibetti et al. (2009; see their Table B1):

[TABLE]

[TABLE]

We utilized Eqn. (2) for 30 of our galaxies, and this was our preferred calibration. Eqn. (3) was applied for the remaining 8 galaxies in our sample. Both equations are reported to have 1$\sigma$ calibration uncertainties of $\approx$0.13 dex. For 17 of the galaxies, both $g-i$ and $B-V$ colors were available. We generated maps based on both calibrations and found good agreement between tracers and consistent with the uncertainty in the Zibetti et al. (2009) calibration.

3.2 Chandra Data Reduction and Catalog Production

For our X-ray point-source measurements, we use Chandra ACIS imaging data (both ACIS-S and ACIS-I) of the galaxies in our sample. In Table 2, we tabulate the full Chandra observing log used in this paper. We restricted our analyses to Chandra data sets that had aim points within 5 arcmin of the central coordinates of the galaxy. This restriction ensures that the ObsID combined images reach deep limits with a sharp PSF ($\;\buildrel<\over{\sim}\;$1.5 arcsec 90% encircled-counts fraction radii) in the central nuclear regions of the galaxies, where source confusion could potentially be problematic. Some of the galaxies in our sample have much more extensive archives than we utilize here. For example, for M81, we make use of only 18 of the 27 ObsIDs that were available in the archive, as a result of us excluding observations from a large program to observe the periphery of the galaxy (PI: D. Swartz).

Our Chandra data reduction was carried out using CIAO v. 4.8 with CALDB v. 4.7.1,222http://cxc.harvard.edu/ciao/ and our procedure followed closely the methods outlined in $\S$2.2 of Lehmer et al. (2017). Briefly, we (1) reprocessed pipeline products using the chandra_repro script; (2) removed bad pixels and columns, and filtered the events list to include only good time intervals without significant ($>$3 $\sigma$) flares above the background level; (3) when applicable, aligned events lists and aspect histograms, via wcs_match and wcs_update, to the deepest Chandra ObsID for a given galaxy, using small translations (median shifts and 1$\sigma$ standard deviations of $\delta$R.A. = $0.16\pm 0.14$ arcsec and $\delta$decl. = $0.16\pm 0.18$ arcsec); (4) constructed merged events lists and astrometric solutions using the merge_obs script; and (5) created additional products, including images, exposure maps, and exposure-weighted PSF maps with a 90% enclosed-count fraction, appropriate for the 0.5–2 keV, 2–7 keV, and 0.5–7 keV bands, which we hereafter refer to as the soft band (SB), hard band (HB), and full band (FB), respectively.

Merged 0.5–7 keV images were searched using wavdetect at a false-positive probability threshold of $1\times 10^{-6}$ over seven wavelet scales from 1–8 pixels in a $\sqrt{2}$ sequence (i.e., 1, $\sqrt{2}$, 2, 2$\sqrt{2}$, 4, 4$\sqrt{2}$, and 8 pixels). We ran wavdetect using the merged exposure maps and 90% enclosed-count fraction PSF maps, which resulted in an initial source catalog with properties (e.g., positions and counts) appropriate for point sources. We inspected images from the three bands (i.e., SB, HB, and FB) by eye with source candidates indicated to ensure this process produced sensible source candidates. We found in the case of M81 that several sources were identified along read-out streaks associated with the piled-up central AGN. Unless the sources were obviously real (based on having spatial count distributions consistent with the PSF and clear multi-band detections), the sources along these streaks were removed from further consideration. Finally, for 14 galaxies, we found that point-source crowding in the central region of the galaxy (near the galactic nuclei) was prohibitively large (e.g., NGC 7552), or the central AGN was bright (e.g., M81). In such cases, we identified circular regions around these sources, within which we excluded the sources, as well as the SFR and $M_{\_}\star$ contributions, from our X-ray luminosity function analyses (see Col. 10 of Table 1). For completeness, these X-ray sources are included in our catalogs with a flag indicating that the source was excluded from our analyses for the above reasons.

Source photometry was computed for all sources using the ACIS Extract (AE) v. 2016sep22 software package (Broos et al. 2010, 2012).333 The ACIS Extract software package and User’s Guide are available at http://www.astro.psu.edu/xray/acis/acis_analysis.html. AE extracts source events and exposure times from all pixels that have exposure within polygonal regions that nominally trace the $\approx$90% encircled counts fraction (ECF). These polygonal contours are constructed by AE, for each source, using 1.497 keV PSFs generated by the MARX v. 5.3.2444http://space.mit.edu/ASC/MARX/ ray-tracing code. In a number of cases, the 90% polygonal regions overlapped, and AE iteratively generated non-overlapping polygonal regions that encompassed a smaller fraction of the PSF, and kept track of those PSF fractions. Local background events files were extracted by AE by first masking the source events within a circular masking region that is 1.1$\times$ the size of the 99.9% ECF at 1.497 keV and then extracting events from a larger circular aperture centered around the sources. The larger circular aperture size is determined by requiring that the summed exposure map value of the background pixels (i.e., those not masked), $T_{\_}{\rm bkg}$, is 5–10 times that determined for the source extraction pixels, $T_{\_}{\rm src}$, and also contains a minimum number of 5 counts. The latter criterion is generally met for $T_{\_}{\rm bkg}=5\times T_{\_}{\rm src}$, but if it is not, then the background aperture is increased up until $T_{\_}{\rm bkg}=10\times T_{\_}{\rm src}$, regardless of whether the aperture contains 5 counts or more.

For sources near the wavdetect threshold, we found that the AE photometry would sometimes provide negative counts in the detection bandpass. Instead of re-evaluating the significance of these sources with AE, and culling low-significance sources from the catalog, we chose to include them and utilize the wavdetect photometry. The primary reason for such discrepancies is likely due to the fact that AE evaluates photometry based on events within the 90% ECF, while wavdetect uses wavelets of various scales to identify sources (sometimes based on scales smaller than the 90% ECF) and reconstructs a model of the source counts. Thus, wavdetect will be somewhat more sensitive than AE in identifying sources when only the core of the PSF is significant compared to the background. Our choice to keep the low-significance sources is also motivated by our later use of wavdetect in calculating the completeness of a given galaxy’s detected sources as a function of counts and location, using large simulations of fake sources (see $\S$3.3 for details). Such completeness calculations are not feasible using the computationally intensive AE photometry procedure.

For sources with $>$20 net counts, we performed basic spectral modeling of the data within AE, using xspec v. 12.9.1 (Arnaud 1996). We adopted an absorbed power-law model with both a fixed component of Galactic absorption and a free variable intrinsic absorption component (TBABS $\times$ TBABS $\times$ POW in xspec). The free parameters include the intrinsic column density, $N_{\_}{\rm H,int}$, and photon index, $\Gamma$. The Galactic absorption column, $N_{\_}{\rm H,gal}$, for each source was fixed to the value appropriate for the location of each galaxy, as derived by Dickey & Lockman (1990).555Galactic column density values were extracted using the colden tool at http://cxc.harvard.edu/toolkit/colden.jsp All spectral fits were derived by minimizing the C-statistic within xspec (Cash 1979), with both the on-source events (i.e., those within the AE extraction regions discussed above) and background events supplied. AE simultaneously fits the background spectrum, using a piecewise linear model, and the on-source spectrum including the background spectrum model plus the physical source model (i.e., the absorbed power law).

For the subsample of sources where spectral fitting was possible, we found median and interquartile ranges of $\log N_{\_}{\rm H,int}=21.3^{+0.5}_{\_}{-0.7}$ and $\Gamma=1.7^{+0.3}_{\_}{-0.5}$. Whenever possible, we computed 0.5–8 keV X-ray fluxes and corresponding luminosities using these best fit models. For sources where spectral fitting was not possible, we converted the 0.5–7 keV count rates to 0.5–8 keV fluxes using the median model (i.e., $\log N_{\_}{\rm H,int}=21.3$ and $\Gamma=1.7$).

In the Appendix, we provide the properties of 4442 X-ray point sources in all 38 galaxies in our sample. Of these X-ray sources, 2478 had $L>10^{35}$ erg s*-1* and were determined to lie within the galactic footprints of our sample. The galactic footprints were taken to be the ellipses that trace the $K_{\_}s\approx 20$ mag arcsec*-2* galactic surface brightness (see Jarrett et al. 2003), with some central regions excised due to the presence of AGN or substantial source crowding. These detailed regions, including exclusion region radii, $r_{\_}{\rm remove}$, are provided in Table 1. The remaining sources were either located outside the $K$-band based regions or within the central regions removed from further analysis (i.e., AGN and clearly crowded sources). We note that a substantial number of sources that we have excluded from our XLF analyses are outside the designated $K_{\_}s\approx 20$ mag arcsec*-2* region, yet within the larger “total” $K_{\_}s$-band ellipse, defined by Jarrett et al. (2003), or the generally larger RC3 regions, defined by de Vaucouleurs (1991). Such sources still have some reasonable probability of being associated with the galaxy, so we report them in our X-ray point-source catalogs; however, their numbers are expected to be small compared with the number of CXB sources in those areas and are therefore not included in our XLF analyses. For convenience, we flag sources in our X-ray catalog that lie within the total $K_{\_}s$-band ellipse, but outside the 20 mag arcsec*-2* ellipse (Flag = 3).

3.3 Catalog Completeness Functions

Since our X-ray data sets span a broad range of Chandra depths, in terms of intrinsic X-ray point-source luminosity, it is essential to understand well the completeness of each of our data sets when fitting XLF models. To address this, we first derive radially-dependent completeness functions for each galaxy using simulations, in which fake sources are added to the FB images and searched for using wavdetect following the prescription adopted in $\S$3.2. For a given galaxy, we generated 700 simulated images in total. Each image consisted of our original 0.5–7 keV Chandra image plus 400 fake X-ray point sources, each of which contained a fixed number of source counts. Each fake X-ray source was placed randomly within the boundaries of a single box in a $20\times 20$ grid of boxes that spanned the image in equal intervals of R.A. and decl. A given simulated image would thus contain 400 fake X-ray sources with one source per box and an equal number of X-ray counts per source. Fifty simulated images were created for each of 14 different choices of simulated source counts with nearly logarithmic spacing (spanning 3–500 source counts). Source counts were probabilistically placed onto the base image using the nearest MARX-based, exposure-weighted PSF that was generated in the AE runs (see $\S$3.2) for the original source catalog. This method was adopted as a practical compromise between running very accurate time-consuming PSF models for a small number of simulated sources and having a robust characterization of the completeness functions based on many sources with slightly inaccurate local PSFs.

To construct the completeness functions themselves we (1) repeated the source detection procedure described in $\S$3.2 for all 700 mock images and (2) compared the mock catalogs with the input catalogs to determine whether a given source was recovered. In a general sense, the completeness functions, for a given galaxy, vary with off-axis angle with respect to the mean aim point and local background and point-source density. In $\S$4 below, we describe how we use our completeness functions when measuring XRB XLFs.

4 X-ray Luminosity Function Measurements

4.1 Galaxy-Wide X-ray Luminosity Function Properties

We began our XLF analyses by fitting the galaxy-wide 0.5–8 keV XLFs for each of the galaxies. As discussed above, we utilized only X-ray point sources and galaxy properties that are appropriate for the regions defined in Table 1, which in some cases means excluding central regions (due to source crowding and AGN). In Figure 3, we display the galaxy-wide observed cumulative XLFs (gray filled circles with 1$\sigma$ Poisson error bars) for the galaxies in our sample. The data used here are simply raw counts, and not corrected for incompleteness. Furthermore, the X-ray point sources will contain contributions from objects that are intrinsic to the galaxies, but also background X-ray point sources from the cosmic X-ray background (CXB; e.g., Kim et al. 2007; Georgakakis et al. 2008) and occasionally foreground stars that are X-ray detected.

We fit the observed galaxy-wide XLFs following a forward-fitting approach, in which we include contributions from the intrinsic X-ray sources (the vast majority of which we expect to be XRBs) and CXB sources, with incompleteness folded into our models. For the intrinsic point-source XLF, we began by fitting the data to single and broken power law models of the respective forms:

[TABLE]

[TABLE]

where $K_{\_}{\rm PL}$ and $\alpha$ are the single power-law normalization and slope, respectively, and $K_{\_}{\rm BKNPL}$, $\alpha_{\_}1$, $L_{\_}b$, and $\alpha_{\_}2$ are the broken power-law normalization, low-luminosity slope, break luminosity, and high-luminosity slope, respectively; both XLF models are truncated above, $L_{\_}c$, the cut-off luminosity. To make the numbers more intuitive, we take $L$, $L_{\_}b$, and $L_{\_}c$ to be in units of $10^{38}$ erg s*-1*, when quoting and describing normalization values. For a given galaxy, we fit the data to determine all constants, except for the break and cut-off luminosities, which we fix at $L_{\_}b=10^{38}$ erg s*-1* and $L_{\_}c=2\times 10^{40}$ erg s*-1*. Also, when the luminosity of the 50% completeness limit (see below for completeness description), $L_{\_}{50}$, was larger than $0.5\times L_{\_}b$, the fit to $\alpha_{\_}1$ was unreliable. For these cases, $\alpha_{\_}1$ was fixed to either 1.2 or 1.6 for galaxies that are respectively below or above sSFR = $10^{-10}$ yr*-1*. Similarly, in some cases, $L_{\_}{50}$ was above the $L_{\_}b$ and $\alpha_{\_}2$ was unreliable. For these cases, $\alpha_{\_}2$ was fixed to either 2.2 or 1.6 for galaxies that are respectively below or above sSFR = $10^{-10}$ yr*-1*.

In principle, we can fit for these values for each galaxy, and we have made attempts to free these parameters; however, in most cases, $L_{\_}b$ is not well constrained, and the best-fit value of $L_{\_}c$ often ends up being a lower limit constraint at the highest luminosity point source for each galaxy. We therefore chose to fix these parameters near sample-averaged values, which we determine in $\S$4.2 below. There are thus three free parameters, namely, $K_{\_}{\rm BKNPL}$, $\alpha_{\_}1$, and $\alpha_{\_}2$.

For the CXB contribution, we implemented a fixed form for the number counts, provided by Kim et al. (2007). The Kim et al. (2007) extragalactic number counts provide estimates of the number of sources per unit area versus 0.5–8 keV flux. The best-fit function follows a broken power-law distribution with parameters derived from the combined Chandra Multiwavelength Project (ChaMP) and Chandra Deep Field-South (CDF-S) extragalactic survey data sets (see Table 4 of Kim et al. 2007). For each galaxy, the number counts were converted to an observed 0.5–8 keV XLF contribution by multiplying the number counts by the areal extent of the galaxy, as defined in Table 1, and converting CXB model fluxes to X-ray luminosities, given the distance to the galaxy.

A complete model of the observed XLF, $dN/dL({\rm obs})$, consists of the intrinsic XLF component, $dN/dL({\rm int})$, e.g., from Equation (4), plus the fixed CXB curve, $dN/dL({\rm CXB})$, convolved with a galaxy-wide weighted completeness function, $\xi(L)$, which was constructed using the radial-dependent completeness functions calculated in $\S$4. Specifically, $\xi(L)$ was calculated by statistically weighting the contributions from the model XLF at each annulus according to the observed distributions of X-ray point sources. Formally, we computed $\xi(L)$ using the following relation:

[TABLE]

where $\xi_{\_}{i}(L)$ is the completeness function for the $i$th annular bin and $w_{\_}i$ is the fraction of total number of galaxy-wide sources within the $i$th annuluar bin based on the observed point-source distributions. For all galaxies, $\xi(L)$ is very close to a monotonically increasing function, although some low-level fluctuations exist due to the nature of our simulations. For points of reference, we quote and utilize two luminosity limits, $L_{\_}{50}$ and $L_{\_}{90}$, which correspond to the point-source luminosity at 50% and 90% completeness (i.e., $\xi(L_{\_}{50})=0.5$ and $\xi(L_{\_}{90})=0.9$). These values are tabulated in Table 3.

We thus modeled the observed XLF using a multiplicative model

[TABLE]

Procedurally, for each galaxy, we constructed the observed $dN/dL({\rm obs})$ using luminosity bins of constant $\delta\log L=0.057$ dex that spanned the range of $L_{\_}{\rm min}=L_{\_}{50}$ to $L_{\_}{\rm max}=5\times 10^{41}$ erg s*-1*. For most galaxies, the majority of the bins contained zero sources, with other bins containing small numbers of sources. As such, we evaluated the goodness of fit using a modified version of the C-statistic (cstat; Cash 1979; Kaastra 2017):

[TABLE]

where the summation takes place over the $n=100$ bins of X-ray luminosity, and $N_{\_}i$ and $M_{\_}i$ are the observed and model counts. We note that when $N_{\_}i=0$, $N_{\_}i\ln(N_{\_}i/M_{\_}i)=0$, and when $M_{\_}i=0$ (e.g., beyond the cut-off luminosity), the entire $i$th term in the summation is zero.

When fitting our data and measuring uncertainties on parameters, we made use of a Markov Chain Monte Carlo (MCMC) procedure that implemented the Metropolis-Hastings sampling algorithm (Hastings 1970). In this procedure, the fitting parameters were first given initial guesses, which we took to be the same set of values for every galaxy. The value of cstat, $C_{\_}{\rm init}$, was computed for this initial guess, and stored. Next, the guesses were perturbed randomly in accordance with a Gaussian distribution with a user-supplied set of standard deviations for each parameter. To begin, we chose the widths of the Gaussians to be large (relative to their likely final distributions) so as to sample parameter space well. The cstat value of the model with perturbed parameters was then computed, $C_{\_}{\rm pert}$, and compared with the value obtained from the previous run and the likelihood ratio, $\mathcal{L}_{\_}{\rm rat}=\exp\{-(C_{\_}{\rm pert}-C_{\_}{\rm init})/2\}$, was evaluated. Next, a random number, $A_{\_}{\rm random}$, between 0 and 1, was drawn and compared with $\mathcal{L}_{\_}{\rm rat}$. If $\mathcal{L}_{\_}{\rm rat}>A_{\_}{\rm random}$, then the new set of parameters was stored, and if $\mathcal{L}_{\_}{\rm rat}\leq A_{\_}{\rm random}$, then the old set of parameters was preserved for subsequent perturbations. Using the current set of stored parameters, the above procedure (i.e., perturbation of parameters, evaluation of $\mathcal{L}_{\_}{\rm rat}$, and comparison with $A_{\_}{\rm random}$) was then repeated 100,000 times, with each iteration using only accepted parameters, to form an initial MCMC chain.

After the 100,000 iterations, we used the initial MCMC chain to compute updated standard deviations of the accepted values, and subsequently ran an additional 900,000 final MCMC iterations, using these standard deviations and the final set of parameters in the initial MCMC chain as a starting point. The distributions of parameter values from the final MCMC chain formed our probability distribution functions (PDFs). Furthermore, additional model-dependent calculated parameter PDFs can be computed by storing their values in MCMC chains. For example, for each model in the MCMC chain, we compute the integrated 0.5–8 keV luminosity, $L_{\_}{\rm X}$:

[TABLE]

where we adopt a lower integration limit of $L_{\_}{\rm lo}=10^{36}$ erg s*-1*.

We note that for a single power-law model, PDFs can be computed with ease using grid-based sampling of the 2D parameter space (i.e., normalization and slope of the power law). We compared PDFs that were computed from such grid-based sampling with those obtained from our MCMC procedure and found essentially identical PDFs. Since we later incorporate more complex models, with up to 7 free parameters ($\S$4.2 below), where the computation time is too large to use a grid-based approach, we chose to use the MCMC procedure consistently throughout this paper.

Hereafter, when quoting best-fit parameter values and uncertainties, we adopt median values from each PDF with 16% and 84% confidence lower and upper limits. In Table 3, we tabulate the best-fit parameter values for the single and broken power-law fits for each each galaxy. In Figure 3, we show the best-fit single (magenta dashed curves) and broken (black solid curves) power-law model cumulative XLFs, which include contributions from the CXB (green dotted curves) and have incompleteness folded in. Goodness of fit was evaluated following the methods outlined in Kaastra (2017), which provides parameterizations of the expected $C$ statistic and its variance for a given model and data binning scheme, so that goodness of fit can be evaluated in an identical way to classical $\chi^{2}$ fitting. For each of our fits, the null hypothesis probability, $P_{\_}{\rm null}$, was calculated as the one minus the probability that the model can be rejected. The values of $P_{\_}{\rm null}$ are listed in Table 3 for both models.

For many galaxies, a single power law provides a statistically acceptable fit to the data (e.g., $P_{\_}{\rm null}>0.01$), with only one of the fits being rejected at the $>$99.9% confidence level ($P_{\_}{\rm null}<0.001$). The majority of the poorest fit cases (e.g., $P_{\_}{\rm null}<0.05$) have a large number of sources detected, due to deep observational data sets. Visual inspection of the fits suggest that some complex structures within the XLFs themselves are not described well with power-laws. Not surprisingly, the broken power-law model provides improvements to the cstat values of the XLFs for many cases; however, in very few cases are the fit improvements statistically significant.

Despite the lack of statistical improvement, we expect that in most cases, the broken power-law fits provide more realistic estimates of the integrated total luminosity, $L_{\_}{\rm X}$, than the single power-law fits. One clear example where the solutions are notably different is illustrated in Figure 4 for NGC 4321 (M100). While statistically, the single and broken power-law fits have very close $P_{\_}{\rm null}$ values to each other, the overall $C$ is notably improved by the broken power-law fit and the calculated $L_{\_}{\rm X}$ values are substantially different between models. We note that this is an extreme case, and that most galaxies have better agreement between $L_{\_}{\rm X}$ values when both models are statistically acceptable. We therefore chose to adopt parameters derived using the broken power-law model, unless either (1) the $C$ value for the broken power law provided no improvement over the single power-law value or (2) the two slopes implied by the broken power-law (i.e., $\alpha_{\_}1$ and $\alpha_{\_}2$) were within 1$\sigma$ of each other. In Table 3, we indicate our adopted model and list $L_{\_}{\rm X}$ based on that model.

In Figure 5, we show the best-fit XLF parameter values versus sSFR for all galaxies in our sample. In terms of trends, $\alpha_{\_}1$ is consistent with being constant across all sSFR values, suggesting little variation in the low-luminosity slope of the XLF for young versus old populations. $\alpha_{\_}2$, on the other hand, exhibits an average decline with increasing sSFR (Spearman’s $\rho$ correlation significance $>$99.95% confidence level), presumably indicating that as the XRB population transitions from LMXBs to HMXBs. If we restrict the sample to massive galaxies (\;\buildrel>\over{\sim}\;$$2\times 10^{10} $M_{\odot}$) or galaxies with substantial SFRs ($\;\buildrel>\over{\sim}\;$2 $M_{\odot}$ yr*-1*), so that the respective LMXB and HMXB population statistics allow for less galaxy-to-galaxy sampling stochasticity (e.g., Gilfanov 2004; Justham & Schawinski 2012; see $\S$5.3 below), we get a clearer sense of this trend (see orange boxes in Fig. 5). Finally, we find that the normalization per unit SFR declines with increasing sSFR, as would be expected as the population shifts from being LMXB dominated at low-sSFR to more HMXB dominated at high-sSFR.

In Figure 6, we show $L_{\_}{\rm X}$/SFR versus sSFR for the sample. As reported by previous authors, this curve shows a clear decline of $L_{\_}{\rm X}$/SFR with increasing sSFR, due to the transition from LMXBs to HMXBs (e.g., Colbert et al. 2004; Lehmer et al. 2010). From Figure 5, it can be inferred that this trend is largely driven by the decline in normalization per unit SFR of the XLF. However, for galaxies where the XLFs are expected to be well sampled (i.e., the orange squares in Figs. 5 and 6), we find a larger range in $K$/SFR than $L_{\_}{\rm X}$/SFR, due to the fact that the high-luminosity-end XLF slope ($\alpha_{\_}2$) becomes shallower for galaxies with high-sSFR (Fig. 5$b$), due to the relatively shallow-sloped HMXB XLF becoming more dominant (e.g., Grimm et al. 2003; M12).

4.2 Global Fit to Specific-SFR Binned Regions

As discussed above, it is expected that the decline in $L_{\_}{\rm X}$/SFR with sSFR is driven by a transition from LMXB to HMXB dominance, and the rate of decline is affected by changes in both XLF normalizations and slopes. Here we examine XLFs in subgalactic regions, selected from the SFR and $M_{\_}\star$ maps discussed in $\S$3.1, to better isolate XRB populations as a function of sSFR, and decompose the XLFs into the SFR-scaled HMXB and $M_{\_}\star$-scaled LMXB components. Hereafter, we make the assumption that the X-ray point source population that is not part of the CXB is dominated by XRBs; however, we note that there will be some contribution from other sources, in particular supernova remnants (SNR) and Galactic stars. Unfortunately, a clean identification of the nature of every point source in our catalog is beyond the scope of this work. However, we expect that the contributions of these sources to the XLFs will be smaller than CXB sources (see, e.g., Fig. 10 of Long et al. 2014 for M83), and will therefore not have a major impact on our conclusions.

To address the above goal, we began by generating local sSFR maps on the pixel scale of our SFR and $M_{\_}\star$ maps. For each pixel, we computed the total SFR and $M_{\_}\star$ within a square $500\times 500$ pc2 region, centered on the pixel. Such pixels have sizes of $3.5\times 3.5$ arcsec2 pixel*-1* for the most distant galaxy in the sample, NGC 5713, to $29.5\times 29.5$ arcsec2 pixel*-1* for the nearest galaxy, M81. Thus each pixel can be used to signify the “local” conditions surrounding a given location, all on the same physical scale. Using these maps, we sorted all pixels for all galaxies into bins of sSFR with bin width, or “resolution,” of $\Delta\log$ sSFR = 0.16 dex, which is the root-mean-square error on the SFR and $M_{\_}\star$ calibration uncertainties (see $\S$2 for details). For the lowest and highest sSFR bins, we required at least one X-ray source be detected within and placed no limits on the respective lower and upper bounds for the inclusion of sSFR pixels in those bins. In total, we identified 21 sSFR bins, continuously covering the sSFR range from \approx$$2.5\times 10^{-13} yr*-1* to \approx$$1.6\times 10^{-9} yr*-1*. The bins contain between 14 and 260 X-ray sources per bin. For each of the sSFR bins, we selected all pixels within the galactic regions (defined in Table 1) that were within the sSFR range of that bin, and calculated the total SFR and $M_{\_}\star$ corresponding to those pixels.

In Figure 7, we show an array of observed SFR-normalized cumulative XLFs for the 21 sSFR bins. From this representation, it is clear that the XRB XLF both declines in normalization per unit SFR and becomes shallower in overall slope with increasing sSFR, as described in $\S$4.1.

Assuming that these trends are driven by changes in the relative LMXB to HMXB populations, we chose to fit all 21 sSFR-binned XLFs globally using a single XLF model that self-consistently describes the contributions from each XRB population. For a given bin of sSFR, the XLF is modeled using the following set of equations:

[TABLE]

[TABLE]

[TABLE]

where Eqn. (11) and (12) mirror Eqn. (3) and (4), respectively. In this case, $K_{\_}{\rm HMXB}$ and $K_{\_}{\rm LMXB}$ are, respectively, normalizations per unit SFR ([$M_{\odot}$ yr*-1*]-1) and $M_{\_}\star$ ([$10^{11}$ $M_{\odot}$]-1) at $L=10^{38}$ erg s*-1*. Here, since our data set is much more expansive than for individual galaxies, we are able to perform fitting for seven parameters: $K_{\_}{\rm LMXB}$, $\alpha_{\_}1$, $L_{\_}b$, $\alpha_{\_}2$, $K_{\_}{\rm HMXB}$, $\gamma$, and $L_{\_}c$. We utilize the same statistical methodology for determining the best fit solution and parameter uncertainties, and minimize $C$ following:

[TABLE]

where $C$ is now determined “globally” through the double summation over all $n_{\_}{\rm sSFR}=$ 21 sSFR bins ($i$th index) and $n_{\_}{\rm X}=100$ X-ray luminosity bins ($j$th index; see $\S$4.1 for details related to luminosity binning).

In Figure 8, we show the best-fit values, PDFs, and parameter correlations for the above model, and in Table 4, we tabulate parameter values from this model. Figure 9 shows the culled differential raw numbers of sources in luminosity bins of $\Delta\log L=0.057$ dex, with Poisson errors plotted (derived following Gehrels 1986). This distribution is compiled from all galaxies in our sample, which have varying Chandra exposures, completeness functions, and properties (e.g., sSFR). In total, our data set contains 2478 X-ray detected point sources. Our model suggests that 1230, 710, and 537 of the sources are LMXBs, HMXBs, and CXB sources, respectively. In a cumulative sense, our overall model (black curve) reproduces very well the raw distribution of source counts, including the complex contours associated with incompleteness. However, our fits are based on minimizing $C$ from Eqn. (13), which requires fitting a decomposition of these data into 21 such curves, binned by sSFR. Using the Kaastra (2017) prescription for evaluating goodness of fit, based on cstat, we find that the best-fit for the 21 sSFR and 100 $L_{\_}{\rm X}$ bins is an acceptable model to the ensemble data set, with $P_{\_}{\rm null}=0.145$.

We further present the calculated parameters,

[TABLE]

and

[TABLE]

two widely used scaling relations, in Figure 8 and Table 4. In Figure 5, we show the model-implied XLF slopes and SFR-normalized XLF normalizations for HMXB and LMXB populations, and in Figure 6, we display the implied $L_{\_}{\rm X}$/SFR vs. sSFR relation based on the $\alpha_{\_}{\rm LMXB}$ and $\beta_{\_}{\rm HMXB}$ model values. For the galaxies where we expect the XLFs to be well sampled (i.e., those with $M_{\_}\star>2\times 10^{10}$ $M_{\odot}$ or SFR $>2$ $M_{\odot}$ yr*-1*; orange boxes in Figs. 5 and 6), we find that the galaxy-by-galaxy XLF parameters follow the global model expectation, in which the high-luminosity slopes ($\alpha_{\_}2$), SFR-normalized XLF normalizations ($K$/SFR), and $L_{\_}{\rm X}$/SFR transition from LMXB-like at low-sSFR to HMXB-like at high-sSFR. Galaxies with lower $M_{\_}\star$ or SFR show more significant scatter away from the average trend, and in $\S$5.3 below, we examine closely the significance of this scatter.

In Figure 7, we display the sSFR-dependent best-fit cumulative XLF model fits to the data, including contributions from LMXB, HMXB, and CXB components. Our model reproduces the trends and basic shapes of these curves well, going from a low-sSFR XLF with relatively high normalization per SFR and broken power-law shape to a high-sSFR XLF with low normalization per SFR and single-sloped power-law shape.

In Figure 10, we show the cumulative XLFs for all 38 galaxies in our sample (same as Fig. 3) with the predicted XLFs from our global model overlaid. That is, the modeled XLF for a given galaxy is generated using our best global solution, which is based on simultaneous fitting to the 21 sSFR-selected subgalactic regions, along with the galaxy-wide completeness function, SFR, $M_{\_}\star$, and sky area. As such, the X-ray data for a given galaxy is not used in these models, aside from its minor influence on the global model solution itself (see below). In Table 5, we provide the cstat value and null-hypothesis probability, $P_{\_}{\rm Null}^{\rm global}$, for the X-ray data for each galaxy, and for convenience of comparison, we re-tabulate the $P_{\_}{\rm Null}$ values from the best-fit single and broken power-law models (Col.(12) and (14), respectively). With a few notable exceptions, which we will discuss in $\S$5.2 below, the global XLF model predicts very well the XLFs of several galaxies (considering the model is not tuned to any one galaxy individually). In fact, for several cases (24 out of the 38), the global model produces an equivalent or better statistical characterization (in terms of $P_{\_}{\rm Null}$; compare Col.(4) with Cols.(12) and (14) in Table 5) of the X-ray data than the best-fit power-law models in $\S$3.2! Some notable cases include NGC3031 (M81), NGC 5194 (M51), NGC 5236 (M83), and NGC 5457 (M101), all of which include more than 100 X-ray sources detected and are better characterized by our global model due to the somewhat complex contours that naturally result from the varying contributions from HMXBs and LMXBs.

To test the level of agreement between our global model and the observed XLFs of each galaxy, we fit a “scaled” version of the global model to each of our galaxies. In this model, we fixed the shape of the model XLF, implied by the global model and the SFR and $M_{\_}\star$ of the galaxy, but varied the normalization of the XLF by a constant factor, $\omega$, such that

[TABLE]

An $\omega=1$, implies no additional scaling of the global model is needed. Using this form of the XRB XLF in the overall model provided in eqn. (10), we fit for only $\omega$ following the procedures defined above. In Figure 11, we display the value of the scaling constant versus NGC name. We find that all but three galaxies (NGC 337, 925, and 4552) have $\omega$ consistent with unity to within a factor of two. For the rest of the galaxies, there is some scatter in $\omega$ around unity (as required by the global moidel fit itself) of $\approx$0.14 dex, which is consistent with the SFR and $M_{\_}\star$ calibration uncertainty (i.e., $\approx$0.16 dex; see gray band in Figure 11). The three galaxies with substantial deviations will be analyzed in more detail in $\S$5.2.

Since the global model describes well the majority of the galaxy XLFs in our sample, it is unlikely that our average XLF scalings suffer from major galaxy-sample variance. However, to test for any notable variations between subsets, we divided our sample into two subsets, retaining the NGC ordering in Table 1, and re-ran our global XLF calculations. In Table 4, we present the results from this run (see “First Subsample” and “Second Subsample” parameters). Although some minor differences are found, the parameters and computed properties ($\alpha_{\_}{\rm LMXB}$ and $\beta_{\_}{\rm HMXB}$) are consistent between subsamples at the 1$\sigma$ level.

5 Discussion

5.1 Comparison with Previous Results and Population Synthesis Models

Our constraints on the HMXB and LMXB XLFs are similar in form to those presented in past works (see, e.g., $\S$1 and references therein). However, as mentioned in $\S$1, this is the first systematic attempt to decompose the XLF into LMXB and HMXB components for a sample of mainly late-type galaxies, regardless of their galaxy-wide sSFR. Furthermore, our XLF analyses contain a somewhat larger sample of galaxies, and include ultradeep data from several galaxies that were not available in past studies. Notably, this provides (1) a unique characterization of the LMXB XLF appropriate for late-type galaxies, which may not necessarily be consistent with the LMXB XLF derived from elliptical galaxies (see $\S$1) and (2) a cleaner characterization of the HMXB XLF shape, down to faint limits. Here, we examine the differences between our XLFs and those reported in the literature.

For the HMXB XLFs, we chose to compare with M12, who derive HMXB parameters based on a 1055 X-ray sources (including $\approx$700 XRBs) in a sample of 29 nearby galaxies with sSFR$~{}>10^{-10}$ yr*-1* in an attempt to avoid LMXB contributions. For the LMXB XLF, we compare with the Z12 study of 20 elliptical galaxies, including a total of 1626 X-ray sources (including $\approx$1580 XRBs).666We note that the M12 and Z12 XLFs were derived using a Salpeter (1955) IMF, which produces SFR and $M_{\_}\star$ values that differ from our Kroupa (2001) IMF by factors of 1.56 and 1.24, respectively. When making comparisons, we have corrected published values by these factors. We also note that the assumed conversion factors that we use here to compute physical properties (e.g., UV plus IR tracer of SFR) differ somewhat from those used by M12 and Z12. M12 make use of Bell (2003) when determining SFR and Z12 utilize Bell & de Jong (2001) for $M_{\_}\star$, while we use Hao et al. (2011) and Zibetti et al. (2009) for SFR and $M_{\_}\star$, respectively. The only non-negligible differences come from the $M_{\_}\star$ conversion factors for the bluest regions, where the Bell & de Jong (2001) $M/L_{\_}K$ is up to a factor of $\sim$10 times higher (although typically much less discrepant) than that used by Zibetti et al. (2009). We have chosen to not make adjustments based on these conversion factors, when comparing XLF properties, due to the complex form and non-trivial influence on the results; however, we point out that some discrepancies between results may in part be due to these assumptions. We note that the Z12 LMXB XLF uses a broken power-law model with two breaks at $L_{\_}{\rm b,1}\approx 5\times 10^{37}$ erg s*-1* and $L_{\_}{\rm b,2}\approx 6\times 10^{38}$ erg s*-1*, instead of the one break at \approx$$5\times 10^{37} erg s*-1* that is used in our model. We experimented with an LMXB XLF that involved two breaks, but found poor constraints on the two separate break locations, and no improvement to the overall quality of the fits to our data. As such, we compare our LMXB XLF parameters $\alpha_{\_}1$, $\alpha_{\_}2$ and $L_{\_}b$ with the Z12 parameters derived below their $L_{\_}{b,2}$ (e.g., our $L_{\_}b$ is compared with their $L_{\_}{b,1}$).

In Figure 8, we highlight comparison parameter values from the literature with blue crosses, representing 1$\sigma$ error bars, as reported in the literature; these comparisons are tabulated in Table 4. We find that the parameters of our LMXB XLF are similar to those of Z12, except that we favor a somewhat higher normalization and steeper faint-end slope ($\alpha_{\_}1$). These differences, combined with our lack of a third steep power-law component at high $L$ yields a somewhat larger estimate for the integrated LMXB X-ray luminosity per unit mass, $\alpha_{\_}{\rm LMXB}$; however, our estimates are consistent with those of Z12 within the uncertainties (see upper right panel in Fig. 8). For the HMXBs, our fit parameters significantly differ from those reported by M12, due primarily to a preference for a steeper slope ($\gamma$) and lower normalization ($K_{\_}{\rm HMXB}$) for our sample. These parameters are anticorrelated in such a way that the integrated X-ray luminosity per unit SFR $\beta_{\_}{\rm SFR}$ is in good agreement with that of M12.

To reveal any unmodeled complex features in the shapes of the XLFs, and more clearly compare differences with those from M12 and Z12, we created Figure 12, which shows our HMXB and LMXB XLFs in differential form. These “clean” HMXB and LMXB XLFs were created by (1) extracting the observed XLFs from regions with sSFR $>10^{-10}$ yr*-1* and sSFR $<3\times 10^{-11}$ yr*-1*, respectively; (2) subtracting the low-level model components related to LMXB and HMXB populations, respectively, as well as the CXB model components; and (3) unfolding our data using the completeness functions generated in $\S$3.3. The data points in Figure 12, represent the unfolded data and 1$\sigma$ Poisson errors in the top panels, and the ratio of the data to our best-fit models in the bottom panels. We further display the M12 and Z12 models for comparisons.

Clearly, the sSFR $>10^{-10}$ yr*-1* HMXB data (Fig. 12$a$) shows a complex shape beyond that described by a simple power-law model. The HMXB XLF can be better described as rapidly declining ($\gamma>1.6$) between $L=10^{36}$–$10^{38}$ erg s*-1*, and following a more exponential-like decline above $L=10^{38}$ erg s*-1*. We found this shape was preserved when changing our sSFR selection limits. For example, the HMXB XLF for regions with $\log$ sSFR = $-10$ to $-9.5$ and $\log$ sSFR $>-9.5$ both show the same basic shapes (see bottom panels of Fig. 12$a$). Such a change in slope of the HMXB XLF has been predicted by previous population synthesis models (e.g., Tzanavaris et al. 2013; Zuo et al. 2014; Artale et al. 2018), and is potentially due to a dominance in wind-fed, young ($\;\buildrel<\over{\sim}\;$20 Myr) BH-HMXBs.

The sSFR $<10^{-10}$ yr*-1* LMXB data (Fig. 12$b$) appear to be generally consistent with the model across the full luminosity range. However, when we examine the data over different sSFR intervals, we see that the residuals are somewhat more complex and indicate that the high-luminosity (L\lower 2.15277pt\hbox{;\buildrel>\over{\sim};}3\times 10^{37} erg s*-1*) LMXB XLF slope gets shallower with increasing sSFR (see bottom panels of Fig. 12$b$). This is consistent with a scenario where higher sSFR regions harbor younger populations of LMXBs that reach higher luminosities than older LMXB populations (e.g., Fragos et al. 2008; Kim & Fabbiano 2010; Lehmer et al. 2014, 2017).

5.2 Variations in the Galaxy-Wide XLFs

As described in $\S$4.2, there are a few galaxies, for which the global model does not provide a good description of the data (see $P_{\_}{\rm Null}$ in Col.(4) of Table 5). For many of these galaxies, the differences between the model and data are within the uncertainties of the SFR or stellar mass calibrations (see Fig. 11), but there are three examples (NGC 337, 925, and 4552) where the XLFs are dramatically discrepant with the model, $P_{\_}{\rm Null}<0.01$, resulting in galaxy luminosities that are dramatically offset from the average relation shown in Figure 6. As detailed by Gilfanov et al. (2004) and Justham & Schawinski (2012), a shallow-sloped XLF can produce large variations in the distributions of bright XRBs, and thus $L_{\_}{\rm X}$, if the XLF is poorly sampled. Such poor XLF sampling is likely to be prevalent in low-SFR galaxies, where the shallow-sloped HMXB XLF will be poorly sampled at the high-$L$ end. To a less important degree, low-$M_{\_}\star$ galaxies, that are dominated by LMXBs (i.e., with low sSFRs), may also suffer from poor XLF sampling, but this is less important than it is for HMXBs, due to the steep XLF slope at high-$L$. Nonetheless, it is instructive to quantify to what degree the XRB XLFs, and implied integrated $L_{\_}{\rm X}$ of our galaxies can be influenced by simple statistical sampling scatter of the HMXB and LMXB XLFs, so that we can identify objects that are clear outliers.

For each galaxy in our sample, we performed a 1000-trial Monte Carlo analysis to construct probability distributions of the summed point-source X-ray luminosity, $L_{\_}{\rm ps}$, as well as the cumulative number of sources detected above $10^{38}$ erg s*-1* and $10^{39}$ erg s*-1*, $N_{\_}{\rm 38}$ and $N_{\_}{\rm 39}$, respectively, assuming that the XRBs in the galaxy follow our global-model XLF (e.g., the black curves in Fig. 10). For a given Monte Carlo trial, we first perturbed the SFR and $M_{\_}\star$ values of a given galaxy (starting with the values in columns 11 and 12 in Table 1) in accordance with a Gaussian distribution of fractional 1$\sigma$ uncertainties of 0.1 and 0.13 dex, respectively, corresponding to the uncertainties on the calibrations (see $\S$3.1). We note that distance-related uncertainties could affect our calculations of SFR, $M_{\_}\star$ and $L$. The median distance-related uncertainty on these quantities is $\approx$0.06 dex (with a range of 0.004–0.2 dex), which is the size of our X-ray luminosity bins and significantly smaller than the calibration uncertainties on SFR and $M_{\_}\star$. Furthermore, since distance-related errors affect SFR and $M_{\_}\star$ in the same way that they affect $L$ (and integrated $L_{\_}{\rm X}$), the impact of the distance-related uncertainties are substantially reduced. We therefore ignore these uncertainties in our simulations. Using the perturbed values of SFR and $M_{\_}\star$, along with our best-fit global model, CXB estimates, and completeness functions, we calculated the numbers of HMXBs, LMXBs, and CXB sources with $L>10^{36}$ erg s*-1* that we would expect to detect.

We perturbed these numbers using Poisson statistics, and calculated numbers of HMXBs, LMXBs, and CXB sources ($N_{\_}{\rm HMXB}^{\rm MC}$, $N_{\_}{\rm LMXB}^{\rm MC}$, and $N_{\_}{\rm CXB}^{\rm MC}$) for the Monte Carlo trial. Using the integrated HMXB, LMXB, and CXB XLF components as probability distributions, we assigned each of the $N_{\_}{\rm HMXB}^{\rm MC}$, $N_{\_}{\rm LMXB}^{\rm MC}$, and $N_{\_}{\rm CXB}^{\rm MC}$ sources luminosity values to construct a simulated list of X-ray point-sources for the trial. The simulated list provides a simulation of the observed XLF, $N_{\_}{\rm ps}(L)$ (e.g., equivalent to the gray data points in Fig. 10), and the source list luminosities can be summed to yield expected total point-source luminosities: $L_{\_}{\rm ps}^{\rm MC}=L_{\_}{\rm LMXB}^{\rm MC}+L_{\_}{\rm HMXB}^{\rm MC}+L_{\_}{\rm CXB}^{\rm MC}$

Our Monte Carlo procedure, run 1000 times per galaxy, thus provides probability distributions of $N_{\_}{\rm ps}(L)$ and $L_{\_}{\rm ps}$. To identify potential outliers, we computed three quantities: $P(L_{\_}{\rm ps})$, $P(N_{\_}{\rm 38})$, and $P(N_{\_}{\rm 39})$, which are the probabilities of observing a population of sources above the measured $L_{\_}{\rm ps}$, $N_{\_}{\rm 38}$, and $N_{\_}{\rm 39}$, respectively, given the model. The values of these probabilities are provided for each galaxy in Col.(5)–(7) of Table 5.

Given that there are 38 galaxies in our full sample, we expect that these probability values may span 0.03\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}P\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}0.97 due to random scatter. Sources outside of this range are good candidates for outliers that do not follow the relation due to some inherently different physical property beyond just statistical variance. For our sample, we find four cases where $P<0.03$: NGC 337, 925, 4552, and 4559. NGC 337, 925, and 4559 are high-sSFR galaxies that show an excess of $L>10^{39}$ erg s*-1* point sources, while NGC 4552 is a low-sSFR elliptical galaxy that shows a significant excess of $L>10^{38}$ erg s*-1* point sources. Figure 13 shows example probability distributions for the three quantities for NGC 925 and NGC 4552, along with their observed values. Comparisons of the properties of these galaxies with the rest of the sample reveal two compelling physical reasons why these galaxies would be offset from the global model distribution: the effects of low-metallicity on HMXB formation or large contributions from GC LMXB populations. Below, we discuss each of these scenarios in turn.

5.2.1 Enhanced HMXBs in Low Metallicity Galaxies

In terms of metallicity, NGC 337, 925, and 4559 are among the five galaxies with the lowest metallicities in our sample, together with NGC 3198 and 4536. These five galaxies have metallicities that are around $\approx$1/2 $Z_{\_}\odot$, factors of 0.4–0.5 times the median metallicity of our sample, and all have relatively small values of $P(N_{\_}{\rm 39})$, indicating a likely excess of luminous sources within the subpopulation. Within this subsample, we detected 12 X-ray point-sources with $L>10^{39}$ erg s*-1*, when $\approx$4 were expected from our global model. From our Monte Carlo simulations, the probability of obtaining 12 sources with $L>10^{39}$ erg s*-1* is $\approx$0.2%, suggesting that the low-metallicity sample as a whole contains an excess of luminous point sources. For comparison, the total point-source luminosity $L_{\_}{\rm ps}$, and number of sources with $L>10^{38}$ erg s*-1*, are consistent with expectations from the global model, $P(L_{\_}{\rm ps})=7$% and $P(N_{\_}{\rm 38})=55$%, respectively, suggesting that the enhanced population is limited to the most luminous sources.

A more detailed view of the low-metallicity XLF is displayed in Figure 14, which shows the combined completeness-corrected, SFR-normalized XLF for the five lowest-metallicity galaxies in our sample. In Figure 14, we overlay our best-fit global model XLF, which includes contributions from HMXBs, LMXBs, and CXB sources (faded blue, red, and green curves). The global model predicts that the XLF of the low-metallicity galaxies is dominated by HMXBs above $L\sim 10^{38}$ erg s*-1*. A factor of $\approx$2–10 times excess of sources over the global model is observed for L\lower 2.15277pt\hbox{;\buildrel>\over{\sim};}5\times 10^{38} erg s*-1* for the low-metallicity subset, with the largest and most significant excess measured around $3\times 10^{39}$ erg s*-1*. Thus, the HMXB XLF of low-metallicity galaxies takes on an enhanced “hump” above the global model at L\lower 2.15277pt\hbox{;\buildrel>\over{\sim};}10^{39} erg s*-1*.

Qualitatively similar enhancements were observed by Basu-Zych et al. (2016, BZ16) in the L\lower 2.15277pt\hbox{;\buildrel>\over{\sim};}10^{40} erg s*-1* XLFs of low-metallicity Lyman-break analog (LBA) galaxies Haro 11 and VV114, and the relatively nearby low-metallicity galaxy NGC 3310 (e.g., Miralles-Caballero et al. 2014) appears to show a similar excess of L\lower 2.15277pt\hbox{;\buildrel>\over{\sim};}10^{38} erg s*-1* sources compared to the M12 relation (see, e.g., Fig. 14 of M12). Using the LBA observations, combined with measurements of $L_{\_}{\rm X}$/SFR versus metallicity from the literature (Basu-Zych et al. 2013a, Brorby et al. 2014; Douna et al. 2015), BZ16 constructed two model scenarios for the low-metallicity XLF consistent with the data. These models include an HMXB XLF that (1) flattens or extends the shallow high-luminosity slope to brighter limits ($\;\buildrel>\over{\sim}\;$1040 erg s*-1*; hereafter “bright-slope”) or (2) increases in normalization, as the metallicity decreases. Both scenarios result in a rise in $L_{\_}{\rm X}$/SFR with decreasing metallicity consistent with the $L>10^{40}$ erg s*-1* LBA XLFs, the HMXB XLF of typical galaxies (based on M12), and the observed $L_{\_}{\rm X}$/SFR versus metallicity correlation, which is also consistent with the Fragos et al. (2013b) population synthesis predictions for the $L_{\_}{\rm X}$/SFR versus metallicity relation.

In Figure 14, we show both BZ16 predictions (i.e., varying bright-slope and normalization with metallicity) for the $\approx$1/2 $Z_{\_}\odot$ HMXB XLF, with model contributions from LMXB and CXB sources added for fair comparison with our data. The bottom-panel of Figure 14 shows the ratio of the low-metallicity galaxy data from this study and BZ16 models compared to our best-fit global model. While the BZ16 models produce elevated HMXB XLF predictions, neither scenario describes well our overall XLF constraints for the $\approx$1/2 $Z_{\_}\odot$ galaxies in our sample. As noted above, the excess of sources in the low-metallicity sample appears to begin at L\lower 2.15277pt\hbox{;\buildrel>\over{\sim};}10^{39} erg s*-1*, roughly an order of magnitude below that in the BZ16 bright-slope model (magenta dot-dashed curve). Furthermore, the BZ16 enhanced normalization model nicely fits the enhanced $L>10^{39}$ erg s*-1* hump, but does not predict the return to the global XLF level at L\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}10^{39} erg s*-1*. It is currently not clear if the overall observed trend of increasing $L_{\_}{\rm X}$/SFR with declining metallicity can be attributed to a smooth development and enhancement of the XLF hump we observe here. It is also possible that more complex changes occur in the HMXB XLF shape with metallicity. Despite this, a more systematic study of how the HMXB XLF varies as a function of metallicity is tractable, but would require a sample of galaxies that span a broader range of metallicity compared to those in this study. Such an investigation, and its implications for XRB population synthesis models, will be the subject of future work.

5.2.2 Enhanced LMXBs in Massive Elliptical Galaxies

In addition to the statistically-significant enhancement of $N_{\_}{39}$ for HMXBs in the lowest-metallicity galaxies in our sample, we also find enhancements in the LMXB populations for some of the early-type galaxies. Most notably, NGC 4552, which has an E-type morphology, is observed to have a statistically significant excess of low-luminosity LMXBs, $N_{\_}{38}$, compared to the global model prediction (see bottom panels of Fig. 13). For massive early-type galaxies like NGC 4552, it has been shown by several authors (e.g., Harris 1991; Bekki et al. 2006; Peng et al. 2008; Harris et al. 2013) that the number of GCs per unit stellar mass can be enhanced and vary significantly from galaxy-to-galaxy. In such galaxies, the contributions from dynamically formed LMXBs coincident with GCs can dominate the XLF of the galaxy (see, e.g., Kim & Fabbiano 2004; Irwin 2005; Juett et al. 2005; Lehmer et al. 2014; Peacock et al. 2017). Although all galaxies in our sample are expected to contain some contributions from GC LMXBs, and our global model will include an average contribution from these GCs that is characteristic of the average number of GCs per unit mass, our global model will not accurately predict the LMXB XLF for galaxies with strong deviations from this average. As previous studies have shown, the galaxies that are most likely to show deviations are massive ellipticals with relatively large dark-matter halos (see, e.g., Harris et al. 2013).

To investigate the relative levels that GC LMXBs are likely contributing to the XLFs in each galaxy, we made use of the Harris et al. (2013) catalog of GC specific frequencies for nearby galaxies. The specific frequency, $S_{\_}N$, for a given galaxy is defined as:

[TABLE]

where $N_{\_}{\rm GC}$ is the number of GCs in the galaxy, and $M_{\_}V^{T}$ is the galaxy-wide total $V$-band absolute magnitude. In a broad sense, $S_{\_}N$, is a proxy for the number of GCs per unit mass. The Harris et al. (2013) catalog contains measurements of the GC populations, including $S_{\_}N$, for a comprehensive sample of 422 nearby galaxies. We found entries for 12 of the 38 galaxies in our sample, and we have added the $S_{\_}N$ values of these galaxies to Table 1. Not surprisingly, measurements were available for the nearest and most massive galaxies in the sample. Given general trends of $S_{\_}N$ versus $M_{\_}\star$, we would expect that the galaxies with available $S_{\_}N$ measurements would be biased toward high-mass galaxies, which tend to have high-$S_{\_}N$. In Figure 15, we display the distribution of $S_{\_}N$ values for the sample, with the median value of $S_{\_}N^{\rm median}=1.1$ indicated. Ten out of the 12 galaxies have $S_{\_}N<2$, while the most significant outlier, NGC 4552, has an $S_{\_}N=7.7$, far above the next highest $S_{\_}N=2.7$ for NGC 4594.

In terms of deviations from the global LMXB XLF, it is interesting to note that the three galaxies with the highest $S_{\_}N$ values, NGC 1404, 4552, and 4594 all have elevated values of $N_{\_}{38}$, with the most extreme galaxy (in $S_{\_}N$ terms), NGC 4552, having a statistically significant enhancement of low-luminosity LMXBs. Given the known enhancements in LMXB populations generated by GC LMXBs, the above strongly implicates contributions from GC LMXBs as being being responsible for the observed excess of LMXBs in NGC 4552 and possibly some of the other galaxies (e.g., NGC 1404 and 4594). A more detailed analysis involving direct identification of GC counterparts (see, e.g., Kim & Fabbiano 2010; Lehmer et al. 2014; Peacock et al. 2017) would be required to quantify the level of influence GCs have on these galaxies. Such a paper is the subject of work currently in preparation (Ferrell et al. 2019, in preparation).

5.3 Characterizing the Statistical Scatter of the Global Model

The above analyses indicate that there are several galaxies that show statistically significant deviations of their XRB populations compared to the global model predictions; however, these deviations are strongly suggested to be attributed to unmodeled dependencies in metallicity and GC LMXB population contributions. In spite of these examples, the global model provides a good characterization of the XLFs for the majority of the galaxies in our sample (see Table 5). We can therefore use the global model to provide good estimates of the typical emission, and scatter-related uncertainty, from XRB populations in galaxies, given their SFR and $M_{\_}\star$ values. However, we note that these calculations are appropriate for galaxies with metallicities and GC specific frequencies close to the average values of our sample: $\langle Z\rangle\approx Z_{\_}\odot$ and $\langle S_{\_}N\rangle\approx 1.5$, respectively.

As a practical matter, for galaxies that are much more distant than those studied here, only the integrated $L_{\_}{\rm X}$ can be measured. In this section, we make use of our global XRB XLF model to predict $L_{\_}{\rm X}$ values, and their potential variations due to scatter, given only SFR and $M_{\_}\star$ values. As discussed at the beginning of $\S$5.2, low-SFR or low-$M_{\_}\star$ populations are subject to large variations in measured $L_{\_}{\rm X}$ due to poorly populated HMXB and LMXB XLFs. For galaxies in these categories, the average scaling relations, $\alpha_{\_}{\rm LMXB}\equiv L_{\_}{\rm X}({\rm LMXB})/M_{\_}\star$ and $\beta_{\_}{\rm HMXB}\equiv L_{\_}{\rm X}({\rm HMXB})$/SFR, are unlikely to give correct estimates of the integrated XRB population luminosities, since these are only accurate when the XLFs are fully populated.

To determine how $L_{\_}{\rm X}$ and its scatter would vary with SFR and $M_{\_}\star$, we followed closely the Monte Carlo procedure outlined above in $\S$5.2. We first generated a grid of 15 sSFR values covering $\log$ sSFR (yr*-1*) = $-12.5$ to $-8.5$ and six $M_{\_}\star$ values ranging from $\log M_{\_}\star(M_{\_}\odot)=$ 9–11.5. These ranges cover broader ranges of galaxy properties than those found in our sample. For a given pairing of sSFR and $M_{\_}\star$, we ran our Monte Carlo simulation (see $\S$5.2 for details) to generate simulated HMXB and LMXB source lists down to a luminosity limit of $L=10^{35}$ erg s*-1*. Here, we did not include completeness functions, as we had done in $\S$5.2 above, since we are interested in the total intrinsic luminosity. Summing the luminosities of the populations gives Monte-Carlo-based estimates of $L_{\_}{\rm X}({\rm HMXB})$, $L_{\_}{\rm X}({\rm LMXB})$, and $L_{\_}{\rm X}$ (i.e., the sum of HMXBs and LMXBs). For a given pair of sSFR and $M_{\_}\star$, we generated a total of 1000 $L_{\_}{\rm X}({\rm HMXB})$, $L_{\_}{\rm X}({\rm LMXB})$, and $L_{\_}{\rm X}$ values each, and constructed probability distribution functions.

In Figures 16$a$ and 16$b$, we display the $L_{\_}{\rm X}({\rm HMXB})$ versus SFR and $L_{\_}{\rm X}({\rm LMXB})$ versus $M_{\_}\star$, respectively, including the expected median (black solid curves) and scatter (i.e., gray shaded regions) in the relations, as well as the $\beta_{\_}{\rm HMXB}$ and $\alpha_{\_}{\rm LMXB}$ scaling relations for fully populated XLFs. For comparison, we include the locations of galaxies that are expected to be HMXB and LMXB dominant, based on having $\log$ sSFR (yr*-1*) $>-9.5$ and $\log$ sSFR (yr*-1*) $<-11.5$, respectively. As expected, the scatter and the deviations of the median $L_{\_}{\rm X}$ from the respective relations grow with decreasing SFR or $M_{\_}\star$ due to the XLF becoming less populated. These effects are larger in the HMXB–SFR scaling than for the LMXB-$M_{\_}\star$ scaling, since the relatively shallow-sloped HMXB XLF leads to large variations in $L_{\_}{\rm X}({\rm HMXB})$, when the XLF is poorly populated. For HMXBs, the median $L_{\_}{\rm X}({\rm HMXB})$ is lower than that implied by $\beta_{\_}{\rm HMXB}$ by more than a factor of two for SFR \lower 2.15277pt\hbox{;\buildrel<\over{\sim};}2 $M_{\odot}$ yr*-1*; all but seven of our galaxies have SFR values in this range. While for LMXBs, the median $L_{\_}{\rm X}({\rm LMXB})$ is a factor of two lower than that implied by $\alpha_{\_}{\rm LMXB}$, only for galaxies with M_{\_}\star\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}3\times 10^{9} $M_{\odot}$; only four of our galaxies have stellar masses in this range. The scatter itself ranges from $\approx$0.3–0.7 dex for HMXBs across SFR= 0.1–10 $M_{\odot}$ yr*-1* and $\approx$0.2–0.4 for LMXBs across $\log M_{\_}\star(M_{\_}\odot)=$ 9.5–11.

In Table 6, we tabulate the results of our Monte Carlo simulations. For a broad range of sSFR and $M_{\_}\star$ combinations, we provide the median (50%), 16%, and 84% confidence ranges for the total $L_{\_}{\rm X}$, which contains contributions from both HMXBs and LMXBs. In Figure 6, we display the 16% and 84% ranges of $L_{\_}{\rm X}$/SFR versus sSFR based on these results for the median stellar mass of our sample $M_{\_}\star=2\times 10^{10}$ $M_{\odot}$ (gray shaded region) and for a low stellar mass bin at $M_{\_}\star=3\times 10^{9}$ $M_{\odot}$ (dotted curves), above which 36 out of the 38 galaxies in our sample lie. As we examined in $\S$5.2.1, the most significant outliers, like NGC 337, 925, 4552, and 4559 are apparent due to their enhanced $L_{\_}{\rm X}$/SFR values over these ranges. Nevertheless, given values of $M_{\_}\star$ and SFR (and thus sSFR), the tabulated values in Table 6 can be used on a galaxy-by-galaxy basis to obtain a realistic estimate of the expected XRB $L_{\_}{\rm X}$ and scatter-related uncertainty. As alluded to throughout all of $\S$ 5, these parameterizations will be improved in the future with studies of how the XLF varies with additional physical properties, such as metallicity and $S_{\_}N$.

6 Summary

In this paper, we have utilized 5.8 Ms of Chandra data, combined with UV–to–IR observations, for 38 nearby (D\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}30 Mpc) galaxies to revisit scaling relations of the HMXB and LMXB XLFs with SFR and $M_{\_}\star$, respectively. We make novel use of local environment to isolate XRB populations in a variety of sSFR bins, which allows us to cleanly determine the HMXB and LMXB XLF shapes and normalizations. In addition to providing new details on XRB XLF scaling relations, which can be applied to a variety of astrophysical problems, this work presents several new data products and results, which we summarize below.

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We present publicly available Chandra data products and catalogs, as well as SFR and $M_{\_}\star$ maps for all 38 galaxies in our sample. These products are constructed carefully following the procedures detailed in $\S$3.

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We report new fits to the XRB XLFs of all 38 galaxies in our sample, including estimates of CXB sources and the intrinsic source populations. We explore how the XLF normalizations, slopes, and calculated XRB luminosities depend on galaxy SFR and $M_{\_}\star$ (see Fig. 5; Table 3). We find that the XLFs show a clear decline in normalization per unit SFR and a decrease in the $L>10^{38}$ erg s*-1* XLF slope with increasing sSFR (i.e., SFR/$M_{\_}\star$), as the dominant XRB population shifts from LMXBs to HMXBs. As a corollary, the integrated XRB luminosity, $L_{\_}{\rm X}$, per unit SFR declines with increasing sSFR (see Fig. 6).

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When analyzing XRB XLFs from subgalactic regions, selected in bins of sSFR, we clearly see the transition in XLF shape and normalization per SFR from the almost “pure” HMXB XLF at sSFR $\approx 5\times 10^{-10}$ yr*-1* to the nearly pure LMXB XLF at sSFR $\approx 10^{-12}$ yr*-1* (see Fig. 7). We present a global model that characterizes the scaling of the HMXB XLF with SFR and LMXB XLF with $M_{\_}\star$ that describes well the data for all 38 galaxies (model curves in Figs. 7 and 9 and Table 4). The parameters of these models and uncertainties are determined using an MCMC procedure and are reported (see Fig. 8 and Table 4).

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We find basic agreement between the HMXB XLF shape and scaling with SFR, as presented in past papers (e.g., M12); however, our HMXB XLF reveals new complex features, beyond the previously reported power-law shape (see Fig. 12$a$) These features include a steep power-law slope between $L\approx 10^{36}$–$10^{38}$ erg s*-1*, a “bump” or “flattening” between $L\approx 10^{38}$–$10^{40}$ erg s*-1*, and rapid fall off at higher luminosities. These features are highly significant and are robustly identified in independent subsets of our data. Similar features have been reported in some XRB population synthesis models of the HMXB XLF.

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We further find qualitatively good agreement between our LMXB XLF with the previously-reported LMXB XLF from Z12, which was based on elliptical galaxies. However, our fits to the data, which is mainly driven by late-type galaxies, prefer a somewhat shallower slope at L\lower 2.15277pt\hbox{;\buildrel>\over{\sim};}10^{39} erg s*-1* and a steeper slope at L\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}10^{38} erg s*-1*. We further find evidence that the LMXB XLF in higher-sSFR subsets is shallower at L\lower 2.15277pt\hbox{;\buildrel>\over{\sim};}10^{39} erg s*-1* and steeper at L\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}10^{38} erg s*-1* compared with our total-sample average (see Fig. 12$b$). We speculate that this is plausibly due to a stellar age effect, in which the LMXB XLF is dominated by older stellar populations at low-sSFR compared to the high-sSFR. This would imply that, compared to older LMXB XLFs, the LMXB XLF for younger populations contains excesses of LMXBs at all luminosities except $L\approx$ $10^{38}$–$10^{39}$ erg s*-1*. Some features of this trend (e.g., more high-$L$ sources) have been predicted in population synthesis models.

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We use our global model and Monte Carlo simulations to identify galaxies that have outlier XLF populations that are statistically significant. We identify four such galaxies: NGC 337, 925, 4552 (M89), and 4559. Scrutiny of these objects indicates that NGC 337, 925, and 4559 are among the lowest metallicity objects in our sample, and NGC 4552 contains a significant excess of GCs per unit optical luminosity (i.e., specific frequency) over all other galaxies in our sample ($\S$5.2).

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To examine the effects of metallicity on the XLFs, we constructed the XLF for the lowest metallicity galaxies in our sample (NGC 337, 925, 3198, 4536, and 4559). We find statistically significant evidence that the HMXB XLF in low-metallicity ($\approx$0.5$Z_{\_}\odot$) galaxies contains an excess of L\lower 2.15277pt\hbox{;\buildrel>\over{\sim};}10^{39} erg s*-1* sources, but comparable numbers of \lower 2.15277pt\hbox{;\buildrel<\over{\sim};}10^{39} erg s*-1* sources, compared to the global average HMXB XLF for our sample, which has a median metallicity \approx$$Z_{\_}\odot (see Fig. 14). This result is in line with other studies that characterize how the integrated X-ray luminosity per SFR is anticorrelated with metallicity (e.g., Basu-Zych et al. 2016; Brorby et al. 2016). Our result provides a first characterization of the $\approx$0.5 $Z_{\_}\odot$ HMXB XLF from $\log L$ (ergs s*-1*) = 37–41.

• •

We conclude that our global model is appropriate for galaxies that are of roughly solar metallicity and have low GC specific frequencies. Finally, with this caveat, we use the global model, along with Monte Carlo simulations to calculate the scatter in the integrated X-ray luminosities of HMXB and LMXB populations as a function of SFR and $M_{\_}\star$. Such a quantity is useful, for example, for X-ray data sets that detect only the total X-ray emission from the galaxy without resolving the XRB populations. We show that the median HMXB and LMXB integrated luminosities deviates substantially (by more than a factor of two) from the XLF-integrated average scaling relations, $L_{\_}{\rm X}$(HMXB)/SFR and $L_{\_}{\rm X}$(LMXB)/$M_{\_}\star$, at SFR \lower 2.15277pt\hbox{;\buildrel<\over{\sim};}2 $M_{\odot}$ yr*-1* and M_{\_}\star\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}3\times 10^{9} $M_{\odot}$, respectively (see Figure 16). The corresponding 16–84% scatter ranges from $\approx$0.3–0.7 dex for HMXBs across SFR= 0.1–10 $M_{\odot}$ yr*-1* and $\approx$0.2–0.4 for LMXBs across $\log M_{\_}\star(M_{\_}\odot)=$ 9.5–11. Characterization of the XRB scatter is provided in Table 6.

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Future investigations are underway to quantitatively assess how metallicity, stellar age, and GC specific frequency affect the XRB XLFs. These studies will provide expansive new constraints on close-binary population synthesis models that are used to understand a variety of close-binary populations (e.g., XRBs, gravitational-wave sources, and millisecond pulsars), and the role of XRBs in environments that are not-yet observable (e.g., during the epoch of heating when HMXBs are thought to dominate the X-ray emissivity of the Universe).

We thank the anonymous referee for their helpful suggestions, which have improved the quality of this paper. We gratefully acknowledge support from the National Aeronautics and Space Administration (NASA) Astrophysics Data Analysis Program (ADAP) grant NNX13AI48G (B.D.L., R.T.E., A.Z.) and Chandra X-ray Center grant GO8-19039X (B.D.L. and A.P.). A.Z. acknowledges funding from the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement n. 617001. Our work includes observations made with the NASA Galaxy Evolution Explorer (GALEX). GALEX is operated for NASA by the California Institute of Technology under NASA contract NAS5-98034. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by NASA and the National Science Foundation (NSF). This work is based on observations made with the Spitzer Space Telescope, obtained from the NASA/IPAC Infrared Science Archive, both of which are operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration. Facilities: Chandra, GALEX, Sloan, 2MASS, Spitzer, Herschel

Appendix A X-ray Point Source Catalog

In Table A1, we provide the X-ray point source catalogs, based on the analyses presented in $\S\S$3.2 and 3.3. The columns include the following: Col.(1): Name of the host galaxy. Col.(2): point-source identification number within the galaxy. Col.(3) and (4): Right ascension and declination of the point source. Col.(5): Offset of the point source with respect to the average aim point of the Chandra observations. Col.(6) and (7): 0.5–7 keV net counts (i.e., background subtracted) and 1$\sigma$ errors. Col.(8)–(9) and (10)–(11): Best-fit column density $N_{\_}{\rm H}$ and photon index $\Gamma$, respectively, along with their respective 1$\sigma$ errors, based on spectral fits to an absorbed power-law model (TBABS $\times$ POW in xspec). For sources with small numbers of counts ($<$20 net counts), we adopted Galactic absorption appropriate for each galaxy and a photon index of $\Gamma=1.7$. Col.(12) and (13): the respective 0.5–8 keV flux and luminosity of the source. Col.(14): Flag indicating the location of the source within the galaxy. Flag=1 indicates the source is within the $K_{\_}s$-band footprint adopted in Table 1, and outside a central region of avoidance, if applicable. All XLF calculations are based on Flag=1 sources. Flag=2 indicates that the source is within the $K_{\_}s$-band footprint, but has a luminosity of $L<10^{35}$ erg s*-1*, and was thus excluded from our XLF analysis. Flag=3 indicates that the source is outside the 20 mag arcsec*-2* $K_{\_}s$-band ellipse of the galaxy, but within the “total” $K_{\_}s$-band ellipse. Flag=4 indicates that the source is located in the central region of avoidance due to either the presence of an AGN or very high levels of source confusion. Flag=5 indicates that the source is outside the “total” $K_{\_}s$-band ellipse.